Higher Dimensional Spacetime Research Articles

String Cloud with Quark Matter and Viscous Fluid Admitting Conformal Motion

This paper addresses the resolution of Einstein’s field equations within a spherically symmetric, higher-dimensional space-time. The solutions incorporate strange quark matter connected to a string cloud with bulk viscous fluid, utilizing the assumption of a one-parameter group of conformal motions. Additionally, the characteristics of these solutions are explored within the context of higher-dimensional spacetime.

Lie symmetries in higher dimensional charged radiating stars

This study investigates the Lie symmetry properties of matter variables, spacetime dimension, and kinematic quantities in spherically symmetric radiating stars undergoing gravitational collapse in higher dimensional spacetimes. Our analysis explores how variations in functions and dependent variables influence the Lie algebra dimensionality and Lie symmetries of the boundary condition. Our study reveals the explicit dependence of charge and spacetime dimension in the Lie symmetry generators for the first time. We examine models with various kinematical features, such as shear, shear-free, geodesic, and non-expanding conditions with different matter variables. Using the Lie symmetries we obtain group invariant solutions to the models and observe how the kinematical features and matter variables affect the Lie symmetries. Additionally, we demonstrate the appearance of a linear equation of state. We recover known four-dimensional models from our results.

Black hole evaporation process and Tangherlini–Reissner–Nordström black holes shadow

In this article, we study the black hole evaporation process and shadow property of the Tangherlini-Reissner-Nordström (TRN) black holes. The TRN black holes are the higher-dimensional extension of the Reissner-Nordström (RN) black holes and are characterized by their mass M, charge q, and spacetime dimensions D. In higher-dimensional spacetime, the black hole evaporation occurs rapidly, causing the black hole’s horizon to shrink. We derive the rate of mass loss for the higher-dimensional charged black hole and investigate the effect of higher-dimensional spacetime on charged black hole shadow. We derive the complete geodesic equations of motion with the effect of spacetime dimensions D. We determine impact parameters by maximizing the black hole’s effective potential and estimate the critical radius of photon orbits. The photon orbits around the black hole shrink with the effect of the increasing number of spacetime dimensions. To visualize the shadows of the black hole, we derive the celestial coordinates in terms of the black hole parameters. We use the observed results of M87 and Sgr A∗ black hole from the Event Horizon Telescope and estimate the angular diameter of the charge black hole shadow in the higher-dimensional spacetime. We also estimate the energy emission rate of the black hole. Our finding shows that the angular diameter of the black hole shadow decreases with the increasing number of spacetime dimensions D.

Dilatonic black holes in dRGT massive gravity

Motivated by high interest in Lorentz invariant massive gravity models known as the dRGT massive gravity, we discuss the dRGT massive gravity including the coupling term between dilaton scalar field and massive graviton, and present static and spherically symmetric solutions of dilatonic black holes in four and higher dimensional spacetime. Later, we investigate phase structure of these black hole solutions, and discover that the dilatonic black hole could possess two horizons, extreme and naked singularity black holes for the suitably parameters values. Calculating the conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics.

Efficiency of magnetic Penrose process in higher dimensional Myers-Perry black hole spacetimes

In this paper, we consider a well-established magnetic Penrose process (MPP) and bring out its impact on the efficiency of energy extraction from higher dimensional (i.e., D>4) black holes. We derive the field equations of motion and determine the expressions for the energy efficiency of energy extraction for the case of higher dimensional black holes. We also examine the efficiency of energy extraction from black holes with (n−1) and n rotations. We demonstrate that black holes with (n−1) rotations has only one horizon, resulting in infinitely large energy efficiency even without MPP. On the other hand, for black holes with n rotations in D>4, the energy efficiency is not infinitely large, but the efficiency can be significantly enhanced by MPP. This enhancement allows for arbitrarily large energy efficiency. We find that the efficiency of energy extraction can exceed 100% for D=5, 6 and D=7, 8 dimensions. Interestingly, for rotation parameters near the extremal value, the energy efficiency remains above 100% in D=7, 8 compared to D=5, 6. MPP can eventually make higher dimensional black holes more efficient even with n rotations. Published by the American Physical Society 2024

Rotational influence on fermions within negative curvature wormholes

In this research, we examine relativistic fermions within the rotating frame of negative curvature wormholes. Initially, as is typical in our context, we introduce the wormholes by embedding a curved surface into a higher-dimensional flat Minkowski spacetime. Subsequently, we derive the spacetime metric that characterizes the rotating frame of these wormholes. We then investigate analytical solutions of the generalized Dirac equation within this framework. Through exploring a second-order non-perturbative wave equation, we seek exact solutions for fermions within the rotating frame of hyperbolic and elliptic wormholes, also known as negative curvature wormholes. Our analysis provides closed-form energy expressions, and we generalize our findings to Weyl fermions. By considering the impact of the rotating frame and curvature radius of wormholes, we discuss how these factors affect the evolution of fermionic fields, offering valuable insights into their behavior.

Communication Protocols and QECC From the Perspective of TQFT, Part II: QECCs as Spacetimes

AbstractTopological quantum field theories (TQFTs) provide a general, minimal‐assumption language for describing quantum‐state preparation and measurement. They therefore provide a general language in which to express multi‐agent communication protocols, e.g., local operations, classical communication (LOCC) protocols. In the accompanying Part I, we construct LOCC protocols using TQFT, and show that LOCC protocols induce quantum error‐correcting codes (QECCs) on the agent‐environment boundary. Such QECCs can be regarded as implementing or inducing the emergence of spacetimes on such boundaries. Here connection between inter‐agent communication and spacetime is investigated, by exploiting different realizations of TQFT. The authors delved into TQFTs that support on their boundaries spin‐networks as computational systems: these are known as topological quantum neural networks (TQNNs). TQNNs, which have a natural representation as tensor networks, implement QECC. The HaPPY code is recognized to be a paradigmatic example. How generic QECCs, as bulk‐boundary codes, induce effective spacetimes is then shown. The effective spatial and temporal separations that take place in QECC enables LOCC protocols between spatially separated observers. The implementation of QECCs in BF and Chern‐Simons theories are then considered, and QECC‐induced spacetimes are shown to provide the classical redundancy required for LOCC. Finally, the topological M‐theory is considered as an implementation of QECC in higher spacetime dimensions.

A new perspective on Kaluza–Klein theories

Assuming that the geometry of spacetime is uniquely determined by the energy–momentum tensor of matter alone, i.e. without any interactions, enables us to construct the Lagrangian from which the metric of higher dimensional spacetime follows. From the geodesic equations that follow, it becomes clear that the incorrect mass of elementary particles predicted by Kaluza–Klein theories arises from the assumption that in the absence of gravity the solution to the Einstein field equations reduces to the Minkowski metric. From construction of a consistent theory of 4D electromagnetism, we find that this assumption does not only result in the incorrect mass of elementary particles, but also the incorrect value of the cosmological constant. This suggests that these incorrect predictions, which are often regarded as major flaws of Kaluza–Klein theories, just reflect the inconsistency of the assumption that the solution to Einstein field equations reduces to Minkowski metric in the absence of gravity and Weyl invariance which is the symmetry of gauge theories in 4D spacetime. Abandoning this assumption results in modification of general relativity. We show that the unified description of fundamental interactions naturally incorporates the Higgs mechanism. For non-Abelian gauge fields, we find that the manifold comprising the extra dimensions has to be a group manifold and show that the standard model is realized in 16D spacetime. We show that charge and spin are the same concept, but what makes them different is that the former follows from symmetry of 4D spacetime while the latter follows from symmetry of the internal space.

Examples of cosmological spacetimes without CMC Cauchy surfaces

CMC (constant mean curvature) Cauchy surfaces play an important role in mathematical relativity as finding solutions to the vacuum Einstein constraint equations is made much simpler by assuming CMC initial data. However, Bartnik (Commun Math Phys 117(4):615–624, 1988) constructed a cosmological spacetime without a CMC Cauchy surface whose spatial topology is the connected sum of two three-dimensional tori. Similarly, Chruściel et al. (Commun Math Phys 257(1):29–42, 2005) constructed a vacuum cosmological spacetime without CMC Cauchy surfaces whose spatial topology is also the connected sum of two tori. In this article, we enlarge the known number of spatial topologies for cosmological spacetimes without CMC Cauchy surfaces by generalizing Bartnik’s construction. Specifically, we show that there are cosmological spacetimes without CMC Cauchy surfaces whose spatial topologies are the connected sum of any compact Euclidean or hyperbolic three-manifold with any another compact Euclidean or hyperbolic three-manifold. Analogous examples in higher spacetime dimensions are also possible. We work with the Tolman–Bondi class of metrics and prove gluing results for variable marginal conditions, which allows for smooth gluing of Schwarzschild to FLRW models.

Reveal the lost entanglement for accelerated atoms in the high-dimensional spacetime

Reveal the lost entanglement for accelerated atoms in the high-dimensional spacetime

Love numbers and Love symmetries for p-form and gravitational perturbations of higher-dimensional spherically symmetric black holes

The static Love numbers of four-dimensional asymptotically flat, isolated, general-relativistic black holes are known to be identically vanishing. The Love symmetry proposal suggests that such vanishings are addressed by selection rules following from the emergence of an enhanced \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} (“Love”) symmetry in the near-zone region; more specifically, it is the fact that the black hole perturbations belong to a highest-weight representation of this near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} symmetry, rather than the existence of the Love symmetry itself, that outputs the vanishings of the corresponding Love numbers. In higher spacetime dimensions, some towers of magic zeroes with regards to the black hole response problem have also been reported for scalar, electromagnetic and gravitational perturbations of the Schwarzschild-Tangherlini black hole. Here, we extend these results by supplementing with p-form perturbations of the Schwarzschild-Tangherlini black hole. We furthermore analytically extract the static Love numbers and the leading order dissipation numbers associated with spin-0 scalar and spin-2 tensor-type tidal perturbations of the higher-dimensional Reissner-Nordström black hole. We find that Love symmetries exist and that the vanishings of the static Love numbers are captured by representation theory arguments even for these higher spin perturbations of the higher-dimensional spherically symmetric black holes of General Relativity. Interestingly, these near-zone \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{SL }\\left(2,{\\mathbb{R}}\\right)$$\\end{document} structures acquire extensions to Witt algebras. Our setup allows to also study the p-form response problem of a static spherically symmetric black hole in a generic theory of gravity. We perform explicit computations for some black holes in the presence of string-theoretic corrections and investigate under what geometric conditions Love symmetries emerge in the near-zone.

Asymptotic Ray Method for the Double Square Root Equation

The parabolic wave equation describes wave propagation in a preferable direction, which is usually horizontal in underwater acoustics and vertical in seismic applications. For dense receiver arrays (receiver spacing is less than signal wavelength), this equation can be used for propagating the recorded wavefield back into the medium for imaging sources and scattering objects. Similarly, for multiple source and receiver array acquisition, typical for seismic exploration and potentially beneficial for ocean acoustics, one can model data in one run using an extension of the parabolic equation—the pseudo-differential Double Square Root (DSR) equation. This extended equation allows for the modeling and imaging of multi-source data but operates in higher-dimensional space (source, receiver coordinates, and time), which makes its numerical computation time-consuming. In this paper, we apply a faster ray method for solving the DSR equation. We develop algorithms for both kinematic and dynamic ray tracing applicable to either data modeling or true-amplitude recovery. Our results can be used per se or as a basis for the future development of more elaborated asymptotic techniques that provide accurate and computationally feasible results.

The role of dimension and electric charge on a collapsing geometry in Einstein–Gauss–Bonnet gravity

The analysis of the continual gravitational contraction of a spherically symmetric shell of charged radiation is extended to higher dimensions in Einstein–Gauss–Bonnet gravity. The spacetime metric, which is of Boulware–Deser type, is real only up to a maximum electric charge and thus collapse terminates with the formation of a branch singularity. This branch singularity divides the higher dimensional spacetime into two regions, a real and physical one, and a complex region. This is not the case in neutral Einstein–Gauss–Bonnet gravity as well as general relativity. The charged gravitational collapse process is also similar for all dimensions N≥5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N\\ge 5$$\\end{document} unlike in the neutral scenario where there is a marked difference between the N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} and N>5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N>5$$\\end{document} cases. In the case where N=5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N=5$$\\end{document} uncharged collapse ceases with the formation of a weaker, conical singularity which remains naked for a time depending on the Gauss–Bonnet invariant, before succumbing to an event horizon. The similarity of charged collapse for all higher dimensions is a unique feature in the theory. The sufficient conditions for the formation of a naked singularity are studied for the higher dimensional charged Boulware–Deser spacetime. For particular choices of the mass and charge functions, naked branch singularities are guaranteed and indeed inevitable in higher dimensional Einstein–Gauss–Bonnet gravity. The strength of the naked branch singularities is also tested and it is found that these singularities become stronger with increasing dimension, and no extension of spacetime through them is possible.

A note on no-hair properties of static black holes in four and higher dimensional spacetimes with cosmological constant

We study no-hair properties of static black holes in four and higher dimensional spacetimes with a cosmological constant. For the vanishing cosmological constant case, we show a no-hair theorem and also a no-short-hair theorem under certain conditions for the energy-momentum of matter fields. For the positive cosmological constant case, we discuss conditions for hairy static black holes to exist in terms of the energy density of matter fields evaluated at the black hole horizon and the cosmological horizon. For the negative cosmological constant case, we study conditions for hairy black holes by presenting a no-hair theorem in which the asymptotic structure is assumed to be determined by the true cosmological constant.

The BMS group in D = 6 spacetime dimensions

The asymptotic structure of gravity in D = 6 spacetime dimensions is described at spatial infinity in the asymptotically flat context through Hamiltonian (ADM) methods. Special focus is given on the Bondi–Metzner–Sachs (BMS) supertranslation subgroup. It is known from previous studies that the BMS group contains more supertranslations as one goes from D = 4 to D = 5. Indeed, while the supertranslations are described by one single function of the angles in D = 4, four such functions are neeeded in D = 5. We consider the case D = 6 with the aim of determining whether the number of supertranslations keeps increasing with the dimension or remains equal to the number found in D = 5. We show that even though there is apparent room for more supertranslations, their number remains equal to the D = 5 value (four): the potentially new supertranslations turn out to define proper gauge transformations corresponding to a redundancy in the description of the system. Critical in the analysis are the boundary conditions chosen to yield a well-defined canonical formalism. Given the computational (but not conceptual) complexity as one increases the dimension, we explicitly discuss the linearized theory and argue that asymptotically, this analysis provides the correct picture. We conclude by considering higher spacetime dimensions where we indicate that the number of physically relevant supertranslations remains equal to four independently of the dimension ⩾5 . Contribution to Stanley Deser memorial volume ‘Gravity, Strings and Beyond’

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

Introducing the Framework of a "Dynamic" Higher Dimensional Spacetime. How Time Behaves in it. Similarities with Quantum Mechanical and Relativistic Behavior

A preliminary study on linear perturbation for a non-minimal derivative coupling scalar-tensor theory

The Cisterna-Delsate-Rinaldi (CDR) model is a variant of scalar-tensor theory that modify gravity by including a term of non-minimal derivative coupling. This model gives interesting aspects in the properties of compact objects, specifically neutron stars. By adjusting one of its parameters, the maximum possible mass of neutron stars can be increased. The authors of the model had also did a perturbation analysis using odd-parity perturbation and following that they also did analysis on the slowly-rotating neutron stars. In this paper, we report our ongoing research on the linear perturbation for the Cisterna model to see its dynamical properties. More precisely, we work on the polar perturbation that affected both the metric and the scalar field, which is different from the axial perturbation used in the slow rotation case. We use higher-dimensional spacetimes to see if the obtained equations will be dimensionally dependent. To simplify calculations for this metric form, we use tetrad method. Currently, we have not succeeded in obtaining the equations of motions in the form of Regge-Wheeler-Zerilli wave equation. The reason is the metric functions cannot be easily decoupled and we find no second derivatives with respect to both time t and radius r in the equations of motion. Only the scalar field can give a wave equation. Further investigation is undergoing.

GEMS Embeddings of Hayward Regular Black Holes in Massless and Massive Gravities

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call ‘massless’. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher-dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity.

Revisiting mass formulas of the four-dimensional Reissner-Nordström-NUT-AdS solutions in a different metric form

Recently, the so-called “consistent thermodynamics” of the Lorentzian Reissner-Nordström (RN)-NUT-AdS4 spacetimes has been pursued by a lot of efforts via different means. Among these attempts, we had proposed a novel idea that “The NUT charge is a thermodynamical multihair” to successfully tackle with the subject. In this paper, we will adopt this strategy to reconsider the mass formulas of the RN-NUT-AdS4 solutions but written in an alternative form, which had not been studied before in any existing literature and might be a most appropriate ansatz for the higher dimensional multiply NUTty-charged AdS spacetimes without any constraint condition. Here, we shall discuss the Christodoulou-Ruffini-like squared mass formula and the first law as well as the Bekenstein-Smarr mass formula by introducing the secondary hair Jn=Mn. For the sake of generality, we have introduced a dimensionless constant w into the constant factor Ξ in the solution expression so that when w=1, all obtained results can reproduce those delivered in our previous work.

Classification of gravitational waves in higher-dimensional space-time and possibility of observation

The direct detection of gravitational waves opens the possibility to test general relativity and its alternatives in the strong field regime. Here we focus on the test of the existence of extra dimensions. The classification of gravitational waves in metric gravity theories according to their polarizations in higher-dimensional space-time and the possible observation of these polarizations in three-dimensional subspace are discussed in this work. We also show that the difference in the response of gravitational waves in detectors with and without extra dimensions can serve as evidence for the existence of extra dimensions.