Solutions Of General Relativity Research Articles

General framework for cyclic and fine-tuned causal models and their compatibility with space-time

Causal modeling is a tool for generating causal explanations of observed correlations and has led to a deeper understanding of correlations in quantum networks. Existing frameworks for quantum causality tend to focus on acyclic causal structures that are not fine-tuned i.e., where causal connections between variables necessarily create correlations between them. However, fine-tuned causal models (which permit causation without correlation) play a crucial role in cryptography, and cyclic causal models can be used to model physical processes involving feedback and may also be relevant in exotic solutions of general relativity. Here we develop a causal modeling framework capable of dealing with these general scenarios. The key feature of our framework is that it allows operational and relativistic notions of causality to be independently defined and for connections between them to be established in a theory-independent manner. The framework first gives an operational way to study causation that allows for cyclic, fine-tuned, and nonclassical causal influences. We then consider how a causal model can be embedded in a space-time structure (modeled as a partial order) and propose a compatibility condition for ensuring that the embedded causal model does not allow signaling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We discuss conditions for preventing superluminal signaling within arbitrary (and possibly cyclic) causal structures and consider models of causation in postquantum theories admitting so-called jamming correlations. Finally, this work introduces the concept of a higher-order affects relation, which is useful for causal discovery in fined-tuned causal models.

The Black Hole Universe, Part I

The original Friedmann (1922) and Lemaitre (1927) cosmological model corresponds to a classical solution of General Relativity (GR), with the same uniform (FLRW) metric as the standard cosmology, but bounded to a sphere of radius R and empty space outside. We study the junction conditions for R to show that a co-moving observer, like us, located anywhere inside R, measures the same background and has the same past light-cone as an observer in an infinite FLRW with the same density. We also estimate the mass M inside R and show that in the observed universe R<rS≡2 GM, which corresponds to a Black Hole Universe (BHU). We argue that this original Friedmann–Lemaitre model can explain the observed cosmic acceleration without the need of Dark Energy, because rS acts like a cosmological constant Λ=3/rS2. The same solution can describe the interior of a stellar or galactic BHs. In co-moving coordinates the BHU is expanding while in physical or proper coordinates it is asymptotically static. Such frame duality corresponds to a simple Lorentz transformation. The BHU therefore provides a physical BH solution with an asymptotically deSitter metric interior that merges into a Schwarzschild metric exterior without discontinuities.

Local solutions of general relativity in the presence of the trace anomaly

Local solutions are a vivid and long-living topic in gravitational physics. We consider exact static pseudo-spherically symmetric solutions of semi-classical Einstein's equations in presence of the trace anomaly contribution. We investigate black hole solutions and propose new metrics describing traversable wormholes. Thanks to the trace anomaly, wormholes are realized in the vacuum and, nevertheless, violate the null energy condition.

The BEHOMO project: Λ Lemaître-Tolman-Bondi N-body simulations

Context. Our universe may feature large-scale inhomogeneities and anisotropies that cannot be explained by the standard model of cosmology, that is, the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker metric, on which the Λ cold dark matter model is built, may not accurately describe observations. Currently, there is not a satisfactory understanding of the evolution of the large-scale structure on an inhomogeneous background. Aims. We have launched the cosmology beyond homogeneity and isotropy (BEHOMO) project to study the inhomogeneous Λ Lemaître-Tolman-Bondi model with the methods of numerical cosmology. Understanding the evolution of the large-scale structure is a necessary step in constraining inhomogeneous models with present and future observables and placing the standard model on more solid ground. Methods. We perform Newtonian N-body simulations, whose accuracy in describing the background evolution is checked against the general relativistic solution. The large-scale structure of the corresponding Λ cold dark matter simulation is also validated. Results. We obtain the first set of simulations of the Λ Lemaître-Tolman-Bondi model ever produced. The data products consist of 11 snapshots between redshift 0 and 3.7 for each of the 68 simulations that have been performed, together with halo catalogs and lens planes relative to 21 snapshots, between redshift 0 and 4.2, for a total of approximately 180 TB of data. Conclusions. We plan to study the growth of perturbations at the linear and nonlinear level, gravitational lensing, and cluster abundances and proprieties.

Deconstructing scaling virial identities in general relativity: Spherical symmetry and beyond

Derrick-type virial identities, obtained via dilatation (scaling) arguments, have a variety of applications in field theories. We deconstruct such virial identities in relativistic gravity showing how they can be recast as self-evident integrals of appropriate combinations of the equations of motion. In spherical symmetry, the appropriate combination and gauge choice guarantee the geometric part can be integrated out to yield a master form of the virial identity as a nontrivial energy-momentum balance condition, valid for both asymptotically flat black holes and self-gravitating solitons, for any matter model. Specifying the matter model we recover previous results obtained via the scaling procedure. We then discuss the more general case of stationary, axisymmetric, asymptotically flat black hole or solitonic solutions in general relativity, for which a master form for their virial identity is proposed, in a specific gauge but regardless of the matter content. In the flat spacetime limit, the master virial identity for both the spherical and axial cases reduces to a balance condition for the principal pressures, discussed by Deser.

Generalized black holes in 3D Kerr-Schild double copy

The double copy of the Coulomb solution in three dimensions is a nonvacuum solution that can be obtained through different matter couplings. It is the static black hole solution of Einstein-Maxwell theory or general relativity minimally coupled to a free scalar field (with one ghost sign in the action in both cases). We consider generalizations of these matter couplings by paying particular attention to the regularity of the static black solution on the gravity side and the corresponding single copy electric field in the gauge theory. We show that (i) Einstein-Born-Infeld theory yields a singular double copy, which admits stable orbits for certain choices of parameters, with a regular single copy electric field, and (ii) black hole solutions constructed by Bueno et al. [Phys. Rev. D 104, L021501 (2021).] by coupling to the scalar field exemplify mostly regular double copies with regular single copy electric fields and also admit stable orbits. Additionally, we use these solutions to investigate the connection between horizons on the gravity side and electric fields on the gauge theory side, which was previously observed in four dimensions.

Black bounces as magnetically charged phantom regular black holes in Einstein-nonlinear electrodynamics gravity coupled to a self-interacting scalar field

The "black-bounce" spacetime geometries, were recently proposed in [A. Simpson, M. Visser, JCAP 02 (2019) 042] as regular black holes that bouncing into a future incarnation of the universe. In this work we will present several black-bounce exact solutions of General Relativity. Among them is a novel type of black-bounce solutions, which in contrast of the Simpson-Visser type [A. Simpson, M. Visser, JCAP 02 (2019) 042], do not have the Ellis wormhole metric as a particular case. The source of these solutions are linear superposition of phantom scalar fields and nonlinear electromagnetic fields.

Comparison of two theories of Type-IIa minimally modified gravity

We investigate two Type-IIa Minimally Modified Gravity theories, namely VCDM and Cuscuton theories. We confirm that all acceptable Cuscuton solutions are always solutions for VCDM theory. However, the inverse does not hold. We find that VCDM allows for the existence of exact General Relativity (GR) solutions with or without the presence of matter fields and a cosmological constant. We determine the conditions of existence for such GR-VCDM solutions in terms of the trace of the extrinsic curvature and on the fields which define the VCDM theory. On the other hand, for the Cuscuton theory, we find that the same set of exact GR solutions (such as Schwarzschild and Kerr spacetimes) is not compatible with timelike configurations of the Cuscuton field and therefore cannot be considered as acceptable solutions. Nonetheless, in Cuscuton theory, there could exist solutions which are not the same but close enough to GR solutions. We also show the conditions to determine intrinsic-VCDM solutions, i.e. solutions which differ from GR and do not belong to the Cuscuton model. We finally show that in cosmology a mapping between VCDM and the Cuscuton is possible, for a generic form of the VCDM potential. In particular, we find that for a quadratic potential in VCDM theory, this mapping is well defined giving an effective redefinition of the Planck mass for the cosmological background solutions of both theories.

Avoidance of Strong Coupling in General Relativity Solutions with a Timelike Scalar Profile in a Class of Ghost-Free Scalar-Tensor Theories

Modified gravity theories can accommodate exact solutions, for which the metric has the same form as the one in general relativity, i.e., stealth solutions. One problem with these stealth solutions is that perturbations around them exhibit strong coupling when the solutions are realized in degenerate higher-order scalar-tensor theories. We show that the strong coupling problem can be circumvented in the framework of the so-called U-DHOST theories, in which the degeneracy is partially broken in such a way that higher-derivative terms are degenerate only in the unitary gauge. In this sense, the scordatura effect is built-in in U-DHOST theories in general. There is an apparent Ostrogradsky mode in U-DHOST theories, but it does not propagate as it satisfies a three-dimensional elliptic differential equation on a spacelike hypersurface. We also clarify how this nonpropagating mode, i.e., the "shadowy" mode shows up at the nonlinear level.

Rigid rotation in GR and a generalization of the virial theorem for gravitomagnetism

In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could be interpreted as a “rigid body” in general relativity and we analyze the different properties respect to the rigidly rotating disk in special relativity: for example, the general relativistic counterpart shows no Doppler effect for a light signal emitted and received from any two points at rest respect to the “rigid body”. This effect can be important to test the validity of the assumed model for our galaxy. In the second part we approach the problem from a low energy expansion perspective and we write down a generalization of the virial theorem for stationary spacetimes. The non-Newtonian contributions can lead to a re-weighting of dark matter in galaxies.

Four-dimensional regular black strings in bilocal gravity

In this paper, we obtain a static black string solution for a bilocal gravitational source in 3+1 dimensions. The solution is regular at the origin and tends asymptotically to the ordinary static uncharged black string solution of general relativity. It allows an event horizon and an internal horizon depending on the value of the mass density. A mass remnant associated with a vanishing Hawking temperature is also found. In order to stabilize the solution, a perfect cosmological fluid with state parameter ω>−1 should be present throughout space. However, energy conditions do not exclude an exotic substance nearby the black string. Finally, we find the stationary counterpart of the solution and analyze the behavior of the horizons according to the mass and angular momentum of the spinning object.

Static and spherically symmetric general relativity solutions in minimal theory of bigravity

We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlev\'e (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates.

Chaotic photon orbits and shadows of a non-Kerr object described by the Hartle–Thorne spacetime

The data from the event horizon telescope have provided a novel view of the vicinity of the horizon of a black hole (BH), by imaging the region around the light-ring. They have also raised hopes for measuring in the near future, features of the image (or the shadow) related to higher order effects of photons travelling in these regions, such as the appearance of higher order bright rings produced by more than one windings of photons around the light-ring. While the prospect of measuring these fine features of Kerr BHs is very interesting in itself, there are some even more intriguing prospects for observing novel features of possible non-Kerr objects, in the case that the subjects of our images are not the BH solutions of general relativity. In the hope of sufficient resolution being available in the future, we explore in this work the structure and properties of null geodesics around a Hartle–Thorne (HT) spacetime that includes a deformation from the Kerr spacetime characterised by the quadrupole deformation δq. These spacetimes have been found to exhibit a bifurcation of the equatorial light-ring to two off-equatorial light-rings in a range of δqs and spin parameters. In addition to this, there is a range of parameters where both the equatorial and the off-equatorial light-rings are present. This results in the formation of a pocket that can trap photon orbits. We investigate the properties of these trapped orbits and find that chaotic behaviour emerges. Some of these chaotic orbits are additionally found to be ‘sticky’ and get trapped close to periodic orbits for long times. We also explore how these novel features affect the shadow and find that the off-equatorial light-rings produce distinctive features that deform its circular shape, while the chaotic behaviour associated to the pocket creates features with fractal structure. These results are shown to be quite general, extending to higher order HT spacetimes.

Non-asymptotically flat Einstein-Scalar black hole

Exact solutions in general relativity and other theories in physics are important. One of such theories is the Einstein-Scalar theory. We present an exact class of solutions in the Einstein-Scalar theory with a specific nonlinear self-interacting potential. The potential admits a local minimum and a local maximum in general configuration. The solutions include AdS and dS black hole and non-black hole spacetimes. The scalar field is regular on and outside the horizon and asymptotically vanishes when We also study the thermal stability of the black hole solution and it is shown that the black hole is thermally stable for a certain interval of the radius of the horizon.

Quasiparticle dynamics by effective pi -field distortion

Modeling dynamical processes of quasiparticles in low dimensional pi -conjugated systems is challenging due to electron-phonon coupling. We show that this interaction leads to linear potential energy terms in the lattice Lagrangian similar to a local “gravitational” field. The presence of quasiparticles deforms this field in a way analogous to a low-dimension solution of general relativity. Our calculations with analytical expressions for effective pi -fields yield the correct band structure and deliver proper time evolution of the quasiparticle’s properties. Furthermore, we report a sharp reduction in the dynamics computational time up to two orders of magnitude, a result that has major simulation implications.

Wormholes and holography: an introduction

Wormholes are intriguing classical solutions in General Relativity, that have fascinated theoretical physicists for decades. In recent years, especially in Holography, gravitational Wormhole geometries have found a new life in many theoretical ideas related to quantum aspects of gravity. These ideas primarily revolve around aspects of quantum entanglement and quantum information in (semi-classical) gravity. This is an introductory and pedagogical review of Wormholes and their recent applications in Gauge-Gravity duality and related ideas.

Shadow and weak gravitational lensing of a rotating regular black hole in a non-minimally coupled Einstein-Yang-Mills theory in the presence of plasma

The null geodesics of the regular and rotating magnetically charged black hole in a non-minimally coupled Einstein-Yang-Mills theory surrounded by a plasma medium is studied. The effect of magnetic charge and Yang-Mills parameter on the effective potential and radius of photon orbits has investigated. We then study the shadow of a regular and rotating magnetically charged black hole along with the observables in presence of the plasma medium. The presence of plasma medium affects the apparent size of the shadow of a regular rotating black hole in comparison to vacuum case. Variation of shadow radius and deformation parameter with Yang-Mills and plasma parameter has examined. Furthermore, the deflection angle of the massless test particles in weak field approximation around this black hole spacetime in presence of homogeneous plasma medium is also investigated. Finally, we have compared the obtained results with Kerr-Newman and Schwarzschild black hole solutions in general relativity (GR).

Compact stars in the Einstein dark energy model

We investigate the properties of high density compact objects in a vector type theory, inspired by Einstein's 1919 theory of elementary particles, in which Einstein assumed that elementary particles are held together by gravitational as well as electromagnetic type forces. From a modern perspective, Einstein's theory can be interpreted as a vector type model, with the gravitational action constructed as a linear combination of the Ricci scalar, of the trace of the matter energy-momentum tensor, and of a massive self-interacting vector type field. To obtain the properties of stellar models we consider the field equations for a static, spherically symmetric system, and we investigate numerically their solutions for different equations of state of quark and neutron matter, by assuming that the self-interaction potential of the vector field either vanishes or is quadratic in the vector field potential. We consider quark stars described by the MIT bag model equation of state and in the Color Flavor Locked phase, as well as compact stars consisting of a Bose-Einstein Condensate of neutron matter, with neutrons forming Cooper pairs. Constant density stars, representing a generalization of the Interior Schwarzschild solution of general relativity, are also analyzed. Also, we consider the Douchin-Haensel (SLy) equation of state. The numerical solutions are explicitly obtained in both standard general relativity, and the Einstein dark energy model and an in depth comparison between the astrophysical predictions of these two theories are performed. As a general conclusion of our study, we find that for all the considered equations of state a much larger variety of stellar structures can be obtained in the Einstein dark energy model, including classes of stars that are more massive than their general relativistic counterparts.

Compact objects in quadratic Palatini gravity generated by a free scalar field

We study the correspondence that connects the space of solutions of General Relativity (GR) with that of Ricci-based Gravity theories (RBGs) of the $f(R,Q)$ type in the metric-affine formulation, where $Q=R_{(\mu\nu)}R^{(\mu\nu)}$. We focus on the case of scalar matter and show that when one considers a free massless scalar in the GR frame, important simplifications arise that allow to establish the correspondence for arbitrary $f(R,Q)$ Lagrangian. We particularize the analysis to a quadratic $f(R,Q)$ theory and use the spherically symmetric, static solution of Jannis-Newman-Winicour as seed to generate new compact objects in our target theory. We find that two different types of solutions emerge, one representing naked singularities and another corresponding to asymmetric wormholes with bounded curvature scalars everywhere. The latter solutions, nonetheless, are geodesically incomplete.

Detectable universes inside regular black holes

While spacetime in the vicinity outside astrophysical black holes is believed to be well understood, the event horizon and the interior remain elusive. Here, we discover a degenerate infinite spectrum of novel general relativity solutions with the same mass-energy and entropy that describe a dark energy universe inside an astrophysical black hole. This regular cosmological black hole is stabilized by a finite tangential pressure applied on the dual cosmological-black hole event horizon, localized up to a quantum indeterminacy. We recover the Bekenstein–Hawking entropy formula from the classical fluid entropy, calculated at a Tolman temperature equal to the cosmological horizon temperature. We further calculate its gravitational quasi-normal modes. We find that cosmological black holes are detectable by gravitational-wave experiments operating within the mu mathrm{Hz}–mathrm{Hz} range, like LISA space-interferometer.