General Relativity Research Articles

Perturbations of Gibbons-Maeda black holes in Einstein-Maxwell-dilaton theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions. Published by the American Physical Society 2024

Rotating Spacetime: Theory or Reality? A Concise Journey of General Relativity

The paper reviews the theoretical formulae of different astrophysical conditions to describe spacetime and connects theory with observational evidence. The spacetime is governed by gravity, which is well-explained by the theory of General Relativity. The paper starts from the simplest version of spacetime, that is, flat spacetime which has no gravitational influence. This spacetime is described by the Minkowski metric. Then the paper goes to the properties of spacetime in the presence of gravity, which creates curved spacetime. The Schwarzschild metric defines this spacetime. Although these phenomena are well-established by experimental proof, the most intricate characteristic of spacetime has not been discovered until very recently. That is the spacetime around a rotating massive body. The paper will present the mathematical expressions for describing such spacetime, the Kerr metric, and finally will end with the observational evidence of the effect of a spinning heavy body around it. Some particular exotic effects such as “frame-dragging" and “ergosphere" will be presented in brief.

Study of isotropic stellar models via durgapal-lake solutions in rastall system

Abstract This manuscript is dealt with the influences of Rastall factor on the physical aspects of isotropic celestial models. In this scenario, both the ideal fluid distribution and static spherically symmetry are taken into consideration. In specifically, the Durgapal-Lake solutions are taken into consideration to analyze the different characteristics of several specific compact star models like Her X-1, Vela X-1, LMC X-4 and RXJ 1856-37. Due to its innovative combination of two methodologies, this solution is a significant advancement on Durgapal-Fuloria and Lake's previous ansatz in enormous crucial eras. Using observed estimates of radii and masses of certain specific star objects, the undefined parameters in Durgapal-Lake ansatz are derived by matching conditions. The consistency of the adopted solutions is examined through the visual interpretation of matter constituents, equation of state factor, energy conditions, mass function and stability criteria corresponding to distinct choices of Rastall factor. The radially symmetric graphs of matter variables as well as the mass function are also displayed. Moreover, We present the graphical analysis for vanishing Rastall factor. It is concluded that in the context of Rastall theory, the stars under examination exhibit stable compositions with Durgapal-Lake solution, while in the context of general relativity, they exhibit instability.

Development of Gravity Theories in the View of TRAPPIST-1e

Abstract Contrary to the solar system, most exoplanet systems detected hitherto are close-in and compact. One typical system is TRAPPIST-1, which has seven nearly co-planar terrestrial planets all within the orbit of Mercury, including three in the habitable zone.
To evaluate the differences in development of sophisticated gravity theories from the solar system, we use N-body integrations to simulate ephemeris and reproduce some important astronomy phenomena observed on the potentially habitable planet TRAPPIST-1e.
Retrograde motions of other planets last 1–2 orders of magnitude shorter than in the solar system, but occur much more frequently. Transit events of all inner planets can be observed steadily. 
Except Kepler's first law is hard to notice for low eccentricities of planets, the other two laws can then be precisely verified in 102 days, because the areas swept by planets vary by <~ 0.01% and the observed semimajor axes and periods result in constants with theoretical and observation accuracies both <~ 2%. However, the mean motion correlation implies the Great Inequality does not keep apparent between one pair of planets like Jupiter and Saturn.
Furthermore, general relativity can hardly be discovered because it gives rise to perihelion precession of inner planets only ∼0.1% of gravity precession, dozens of times smaller than Mercury. 
Our results supports the possibility of developing part of gravity theories by potential exo-civilizations in compact systems like TRAPPIST-1.

Closed causal curves in f(ℛ,𝒜,AμνAμν) gravity

In this paper, we investigate a [Formula: see text] solution of Einstein field equations, an extension of [Formula: see text] Misner space in the context of Ricci-inverse ([Formula: see text])-gravity theory. For that, we consider two different class, namely, Class-II model which is defined by the function [Formula: see text] and Class-III model defined by the function [Formula: see text]. Here, [Formula: see text] is the anti-curvature tensor with [Formula: see text] as its scalar, and [Formula: see text] is the Ricci scalar. Using this [Formula: see text] metric as background, the modified field equations for Ricci-inverse gravity were derived and obtain the results. These derived field equations are then solvable by choosing the pure radiation field as the energy-momentum tensor, including a cosmological constant as does in the general relativity. This implies that the chosen [Formula: see text] space-time is a valid solution in this novel gravity theory, and thereby violate the causality condition, analogous to general relativity.

Schouten-Codazzi Gravity

Abstract We propose a new phenomenological second order gravity theory to be denoted as ''Schouten-Codazzi' Gravity'' (SCG), as it is based on Schouten and Codazzi tensors. The theory is related, but is clearly distinct from Cotton Gravity. By assuming as source the energy momentum of General Relativity, we form a second order system with its geometric sector given by the sum of the Schouten tensor and a generic second order symmetric tensor complying with the following properties: (i) it must satisfy the Codazzi differential condition and (ii) it must be concomitant with the invariant characterization based on the algebraic structure of curvature tensors for specific spacetimes or classes of spacetimes. We derive and briefly discuss the properties of SCG solutions for static spherical symmetry (vacuum and perfect fluid), FLRW models and spherical dust fluids. While we do recognize that SCG is ``work in progress'' in an incipient stage that still requires significant theoretical development, we believe that the theory provides valuable guidelines in the search for alternatives to General Relativity

The Witten Deformation of the Non-Minimal de Rham–Hodge Operator and Noncommutative Residue on Manifolds with Boundary

Under the announcement by Alain Connes that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein–Hilbert action of general relativity, we derive the Lichnerowicz-type formula for the Witten deformation of the non-minimal de Rham–Hodge operator and the gravitational action in the case of n-dimensional compact manifolds without boundary. Finally, we present the proof of the Kastler–Kalau–Walze-type theorem for the Witten deformation of the non-minimal de Rham–Hodge operator on four- and six-dimensional oriented compact manifolds with boundary.

Systematic bias due to mismodeling precessing binary black hole ringdown

Accurate waveform modeling is crucial for parameter estimation in gravitational wave astronomy, impacting our understanding of source properties and the testing of general relativity. The precession of orbital and spin angular momenta in binary black hole (BBH) systems with misaligned spins presents a complex challenge for gravitational waveform modeling. Current precessing BBH waveform models employ a coprecessing frame, which precesses along with the binary. In this paper, we investigate a source of bias stemming from the mismodeling of ringdown frequency in the coprecessing frame. We find that this mismodeling of the coprecessing frame ringdown frequency introduces systematic biases in parameter estimation, for high-mass systems in particular, and in the inspiral-merger-ringdown (IMR)-consistency test of general relativity. Employing the waveform model henom, we conduct an IMR-consistency test using a Fisher matrix analysis across parameter space, as well as full injected signal parameter estimation studies. Our results show that this mismodeling particularly affects BBH systems with high-mass ratios, high-spin magnitudes, and highly inclined spins. These findings suggest inconsistencies for all waveform models which do not address this issue. Published by the American Physical Society 2024

Measurement of the Weyl potential evolution from the first three years of dark energy survey data.

The Weyl potential, which is the sum of the spatial and temporal distortions of the Universe's geometry, provides a direct way of testing the theory of gravity and the validity of the ΛCDM (Lambda Cold Dark Matter) model. Here we present measurement of the Weyl potential at four redshifts bins using data from the first three years of observations of the Dark Energy Survey. We find that the measured Weyl potential is 2 σ, respectively 2.8 σ, below the ΛCDM predictions in the two lowest redshift bins. We show that these low values of the Weyl potential are at the origin of the tension between Cosmic Microwave Background measurements and weak lensing measurements, regarding the parameter σ8 which quantifies the clustering of matter. Interestingly, we find that the tension remains if no information from the Cosmic Microwave Background is used. Dark Energy Survey data on their own prefer a high value of the primordial fluctuations, together with a slow evolution of the Weyl potential. An important feature of our method is that the measurements of the Weyl potential are model-independent and can therefore be confronted with any theory of gravity, allowing efficient tests of models beyond General Relativity.

Geometric Relational Framework for General‐Relativistic Gauge Field Theories

AbstractIt is recalled how relationality arises as the core insight of general‐relativistic gauge field theories from the articulation of the generalized hole and point‐coincidence arguments. Hence, a compelling case for a manifestly relational framework ensues naturally. A formulation for such a framework is proposed, based on a significant development of the dressing field method of symmetry reduction. A version for the group of automorphisms of a principal bundle over a manifold is first developed, as it is the most natural and elegant, and as hosts all the mathematical structures relevant to general‐relativistic gauge field theory. However, as the standard formulation is local, on , the relational framework for local field theory is then developed. The generalized point‐coincidence argument is manifestly implemented, whereby the physical field‐theoretical degrees of freedoms co‐define each other and define, coordinatize, the physical spacetime itself. Applying the framework to General Relativity, relational Einstein equations are obtained, encompassing various notions of “scalar coordinatization” à la Kretschmann–Komar and Brown–Kuchař.

1/c deformations of AdS3 boundary conditions and the Dym hierarchy

Abstract This work introduces a novel family of boundary conditions for AdS3 General Relativity, constructed through a polynomial expansion in negative integer powers of the Brown-Henneaux central charge. The associated dynamics is governed by the Dym hierarchy of integrable equations. It is shown that the infinite set of Dym conserved charges generates an abelian asymptotic symmetry group. Additionally, these boundary conditions encompass black hole solutions, whose thermodynamic properties are examined.

Gauge invariant perturbations of static spatially compact LRS II spacetimes

Abstract We present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by construction covariant and identification gauge invariant and encompass the geometry and the thermodynamics of the fluid sources. The new equations are then applied to the study of isotropic, adiabatic perturbations. We discuss how the choice of frame in which perturbations are described can significantly simplify the mathematical analysis of the problem and show that it is possible to change frames directly from the linear level equations. We find explicitly that the case of isotropic, adiabatic perturbations can be reduced to a singular Sturm–Liouville eigenvalue problem, and lower bounds for the values of the eigenfrequencies can be derived. These results lay the theoretical groundwork to analytically describe linear, isotropic, and adiabatic perturbations of static, spherically symmetric spacetimes.

Pythagoreanism and Modern Models of Cosmology

Turning to the accumulated philosophical knowledge, the scientist almost always discovers that there are ideas in it which are far ahead of their time, but which can help in solving scientific problems of quite another historical epoch. In this respect one of the most revealing examples are associated with the discovery of heliocentrism and the General Theory of Relativity. Philosophical ideas and principles immanent in one or another particular science and serving for the solution of some problem of it form the very philosophical foundations of the given science. These, in turn, are by no means identical with the whole body of knowledge which philosophy creates. By reflecting on the foundations of science and turning to the analysis of its arbitrary forms – namely cosmology – philosophical reflection elaborates ideas and principles that can play an essential role in a certain stage of scientific inquiry.

Einstein’s spacetime curvature and gravitational waves: Elucidating the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation

In the general theory of relativity initially rationalized by Einstein, the gravity is considered as an occurrence ensuing from the spacetime curvature, which is in turn triggered by the presence of mass. This article provides a detailed analysis of spacetime curvature and gravitational waves, enhancing our understanding of general relativity and astrophysics. Using both analytical and numerical methods, we examined the gradient flow of scalar invariants, variations in the Ricci scalar, and gravitational wave propagation. New findings include the identification of unique curvature patterns around rotating black holes, a detailed comparison of gradient flow behavior in different spacetime geometries, and the discovery of a correlation between scalar invariant fluctuations and gravitational wave amplitudes. These findings validate numerical techniques and reveal how different parameters affect gravitational wave characteristics. While simplified models are used, the present study offers a robust framework for future research. Our work aligns with previous studies but also reveals unique aspects of wave behavior, with implications for quantum gravity and cosmology.

Existence and absence of Killing horizons in static solutions with symmetries

Abstract Without specifying a matter field nor imposing energy conditions, we study Killing horizons in $n(\ge 3)$-dimensional static solutions in general relativity with an $(n-2)$-dimensional Einstein base manifold. Assuming linear relations $p_{\rm r}\simeq\chi_{\rm r} \rho$ and $p_2\simeq\chi_{\rm t} \rho$ near a Killing horizon between the energy density $\rho$, radial pressure $p_{\rm r}$, and tangential pressure $p_2$ of the matter field, we prove that any non-vacuum solution satisfying $\chi_{\rm r}<-1/3$ ($\chi_{\rm r}\ne -1$) or $\chi_{\rm r}>0$ does not admit a horizon as it becomes a curvature singularity. For $\chi_{\rm r}=-1$ and $\chi_{\rm r}\in[-1/3,0)$, non-vacuum solutions admit Killing horizons, on which there exists a matter field only for $\chi_{\rm r}=-1$ and $-1/3$, which are of the Hawking-Ellis type~I and type~II, respectively. Differentiability of the metric on the horizon depends on the value of $\chi_{\rm r}$, and non-analytic extensions beyond the horizon are allowed for $\chi_{\rm r}\in[-1/3,0)$. In particular, solutions can be attached to the Schwarzschild-Tangherlini-type vacuum solution at the Killing horizon in at least a $C^{1,1}$ regular manner without a lightlike thin shell. We generalize some of those results in Lovelock gravity with a maximally symmetric base manifold.

Well-balanced High-order Finite Difference Weighted Essentially Nonoscillatory Schemes for a First-order Z4 Formulation of the Einstein Field Equations

We develop a new class of high-order accurate well-balanced finite difference (FD) weighted essentially nonoscillatory (WENO) methods for numerical general relativity (GR), which can be applied to any first-order reduction of the Einstein field equations, even if nonconservative terms are present. We choose the first-order nonconservative Z4 formulation of the Einstein equations, which has a built-in cleaning procedure that accounts for the Einstein constraints and that has already shown its ability in keeping stationary solutions stable over long timescales. By introducing auxiliary variables, the vacuum Einstein equations in first-order form constitute a partial differential equation system of 54 equations that is naturally nonconservative. We show how to design FD-WENO schemes that can handle nonconservative products. Different variants of FD WENO are discussed, with an eye to their suitability for higher-order accurate formulations for numerical GR. We successfully solve a set of fundamental tests of numerical GR with up to ninth-order spatial accuracy. Due to their intrinsic robustness, flexibility, and ease of implementation, FD-WENO schemes can effectively replace traditional central finite differencing in any first-order formulation of the Einstein field equations, without any artificial viscosity. When used in combination with well-balancing, the new numerical schemes preserve stationary equilibrium solutions of the Einstein equations exactly. This is particularly relevant in view of the numerical study of the quasi-normal modes of oscillations of relevant astrophysical sources. In conclusion, general relativistic high-energy astrophysics could benefit from this new class of numerical schemes and the ecosystem of desirable capabilities built around them.

Beyond the Hellings–Downs curve: Non-Einsteinian gravitational waves in pulsar timing array correlations

Pulsar timing arrays (PTAs) have revealed galaxy-size gravitational waves (GWs) in the form of a stochastic gravitational wave background (SGWB), correlating the radio pulses emitted by millisecond pulsars. This discovery naturally leads to the question of the origin and the nature of the SGWB; the latter is synonymous to testing how quadrupolar the inter-pulsar spatial correlation is. In this paper, we investigate the nature of the SGWB by considering correlations beyond the Hellings–Downs (HD) curve of Einstein’s general relativity. We scrutinize the HD and non-Einsteinian GW correlations with the North American Nanohertz Observatory for Gravitational Waves and the Chinese PTA data, and find that both data sets allow a graviton mass of mg ≲ 1.04 × 10−22 eV/c2 and subluminal traveling waves. We discuss gravitational physics scenarios beyond general relativity that could host non-Einsteinian GW correlations in the SGWB and highlight the importance of the cosmic variance inherited from stochastic variations across realizations in interpreting PTA observations.

Mass Inflation without Cauchy Horizons.

Mass inflation is a well established instability, conventionally associated to Cauchy horizons (which are also inner trapping horizons) of stationary geometries, leading to a divergent exponential buildup of energy. We show here that finite (but often large) exponential buildups of energy are present for dynamical geometries describing accreting black holes with slowly evolving inner trapping horizons, even in the absence of Cauchy horizons. The explicit evaluation of the adiabatic conditions behind these exponential buildups shows that this phenomenon is universally present for physically reasonable accreting conditions. This noneternal mass inflation does not require the introduction of global spacetime concepts. We also show that various known results in the literature are recovered in the limit in which the inner trapping horizon asymptotically approaches a Cauchy horizon. Our results imply that black hole geometries with nonextremal inner horizons, including the Kerr geometry in general relativity, and nonextremal regular black holes in theories beyond general relativity, can describe dynamical transients but not the long-lived end point of gravitational collapse.

The power spectrum of luminosity distance fluctuations in General Relativity

At low redshift, it is possible to combine spectroscopic information of galaxies with their luminosity or angular diameter distance to directly measure the projection of peculiar velocities (PV) along the line-of-sight. A PV survey probing a large fraction of the sky is subject to so-called wide-angle effects, arising from the variation of the line-of-sight across the sky, and other sub-leading projection effects due to the propagation of the photons in a perturbed cosmological background. In this work, for the first time, we provide a complete description, within linear theory and General Relativity, of the power spectrum of luminosity distance fluctuations, clarifying its relation to the observables in a PV survey. We find that wide-angle effects will be detected at high significance by future observations and will have to be included in the cosmological analysis. Other relativistic projections effects could also be detected provided accurate, per object, distances are available.

Thermodynamics and quasinormal modes of the Dymnikova black hole in higher dimensions

In this study, we investigate the thermodynamic properties and quasinormal modes of Dymnikova black holes within the context of higher dimensions in Einstein’s general theory of relativity. We calculate the thermodynamic parameters, including the Hawking temperature and heat capacity, which allowed us to investigate the black hole’s stability. Lastly the quasinormal modes with the WKB formula were calculated.