arXiv subjects

Emel Altas

Publications and source records attributed to Emel Altas.

At least 19 recordsLinked to original sources

arXiv2026

Conserved Gravitational Charges as Curvature Fluxes

Conserved gravitational charges are commonly expressed as surface integrals of the metric perturbation and its first derivatives. We show that, in the usual asymptotically AdS and asymptotically flat settings, the standard charges admit equivalent representatives as fluxes of linearized curvature. The construction uses a divergence-free rank-four tensor whose trace is proportional to the cosmological Einstein tensor. On a maximally symmetric AdS background, it reproduces the known curvature representation of the Abbott-Deser charges. The asymptotically flat construction is not obtained by taking a naive $\Lambda \rightarrow 0$ limit, since the Killing two-form vanishes for translations. We instead introduce an antisymmetric Poincar\'e Killing potential. A representative Killing potential adapted to the algebraic Bianchi identity converts the linearized Einstein current into a total divergence and yields a single curvature-flux formula. Its translation sector reproduces the ADM energy--momentum, while in four dimensions its Lorentz sector reproduces the angular momentum and boost/center-of-mass charges under the standard Regge-Teitelboim falloff and parity conditions. The normalization is checked explicitly for Schwarzschild, boosted Schwarzschild, and Kerr data. On non-maximally symmetric Einstein backgrounds, background Weyl curvature generates additional terms, so the maximally symmetric construction does not directly extend to a pure codimension-two curvature-flux formula.

gr-qc↗

arXiv2026

Static Tidal Perturbations of Relativistic Stars: Corrected Center Expansion and Love Numbers-I

We revisit static tidal perturbations of relativistic stars with emphasis on two technical issues in the standard quadrupolar formulation. First, we derive the regular-center Frobenius expansion of the interior even-parity master function and obtain a corrected subleading coefficient, which differs from the expression commonly used in the literature. Second, we derive the static even-parity master equation on a Schwarzschild-de Sitter background, extending the usual asymptotically flat problem to a two-horizon geometry. To place these results on a common footing, we also show how the general interior even-parity system in Regge-Wheeler gauge reduces to the standard quadrupolar equation used in Love-number calculations. Numerical integrations for polytropic equations of state show that the corrected center coefficient affects only subleading initial data and leaves the extracted Love number $k_2$ unchanged within numerical accuracy. Taken together, these results fix the regular-center input to the standard quadrupolar problem and extend the static even-parity formalism to Schwarzschild-de Sitter backgrounds.

gr-qc↗

arXiv2026

Geometry is Wavy: Curvature Wave Equations for Generic Affine Connections

Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor obeys a wave equation of the schematic form \[ \Box Riem=\mathcal{Q}(Riem,Riem), \] where $\mathcal{Q}(Riem,Riem)$ denotes the terms quadratic in the curvature arising from the Bianchi identities. In this work, we generalize this curvature wave equation to spacetimes endowed with a generic affine connection possessing torsion and nonmetricity. Working within the metric-affine framework, we derive the corresponding wave equation for the Riemann tensor and analyze its structure in several geometrically and physically distinguished settings, including Einstein spaces, teleparallel gravity, and Einstein-Cartan theory.

gr-qc↗

arXiv2025

Consistency Problems of Conformal Killing Gravity

We show that gravity field equations based on a tensor with rank greater than 2 have consistency problems in the sense that integration constants in the solutions, such as the parameter $m$ in the Schwarzschild metric, do not allow for an interpretation in terms of conserved quantities in the theory. The recently introduced Conformal Killing Gravity, an interesting extension of General Relativity that inherits all the solutions of the latter, and defined with a rank-3 tensor field equation that does not arise from a diffeomorphism-invariant action, is plagued with this problem. In this theory, it is not clear at all how one can define the energy and angular momentum for black hole solutions, or define the analogues of the formulas, such as the quadrupole formula, in the weak field limit for gravitational waves emitted by compact sources.

gr-qc↗

arXiv2024

Vanishing of Conserved Charges in Cotton Gravity

Cotton gravity was recently introduced as a higher derivative extension of General Relativity. The field equations of the theory involve the rank-3 Cotton tensor. Here we show that all solutions of the theory, including the black holes, have vanishing conserved charges, i.e. mass and angular momentum. This result implies that either the theory is unphysical since all the black holes carry the charges of the vacuum and can be created at no energy cost, or the theory has confinement of mass/energy and all other conserved quantities.

gr-qc↗

arXiv2024

Constraints and Time Evolution in Generic $f$(Riemann) Gravity

We give a detailed canonical analysis of the $n$-dimensional $f$(Riemann) gravity, correcting the earlier results in the literature. We also write the field equations in the Fischer-Marsden form which is amenable to identifying the non-stationary energy on a spacelike hypersurface. We give pure $R^{2}$ and $R_{\mu\nu}R^{\mu\nu}$ theories as examples.

gr-qc↗

arXiv2023

Non-stationary Energy of Perfect Fluid Sources in General Relativity

The ADM energy for asymptotically flat spacetimes or its generalizations to asymptotically non-flat spacetimes measure the energy content of a stationary spacetime, such as a single black hole. Such a stationary energy is given as a geometric invariant of the spatial hypersurface of the spacetime and is expressed as an integral on the boundary of the hypersurface. For non-stationary spacetimes, there is a refinement of the ADM energy, the so-called Dain's invariant that measures the non-stationary part, the gravitational radiation component, of the total energy. Dain's invariant uses the metric and the extrinsic curvature of the spatial hypersurface together with the so-called approximate Killing initial data and vanishes for stationary spacetimes. In our earlier work [Phys.Rev.D 101 (2020)2, 024035], we gave a reformulation of the non-stationary energy for vacuum spacetimes in the Hamiltonian form of General Relativity written succinctly in the Fischer-Marsden form. That formulation is relevant for merging black holes or other compact sources. Here we extend this formulation to non-vacuum spacetimes with a perfect fluid source. This is expected to be relevant for spacetimes that have a compact star, say a neutron star colliding with a black hole or another non-vacuum object.

gr-qc↗

arXiv2022

Hawking Temperature as the Total Gauss-Bonnet Invariant of the Region Outside a Black Hole

We provide two novel ways to compute the surface gravity ($\kappa$) and the Hawking temperature $(T_{H})$ of a stationary black hole: in the first method $T_{H}$ is given as the three-volume integral of the Gauss-Bonnet invariant (or the Kretschmann scalar for Ricci-flat metrics) in the total region outside the event horizon; in the second method it is given as the surface integral of the Riemann tensor contracted with the covariant derivative of a Killing vector on the event horizon. To arrive at these new formulas for the black hole temperature (and the related surface gravity), we first construct a new differential geometric identity using the Bianchi identity and an antisymmetric rank-$2$ tensor, valid for spacetimes with at least one Killing vector field. The Gauss-Bonnet tensor and the Gauss-Bonnet scalar play a particular role in this geometric identity. We calculate the surface gravity and the Hawking temperature of the Kerr and the extremal Reissner-Nordstr\"om holes as examples.

gr-qc↗

arXiv2021

Anomalous Dispersion in Gravity Theories

A wave pulse (be it a gravitational wave or a light wave) undergoes anomalous dispersion in a vacuum in flat spacetimes with an even number of spatial dimensions even if all the frequencies move at the same speed. Such an anomalous dispersion does not occur in spacetimes with an odd number of spatial dimensions. We study various gravity theories and show that dispersion-free propagation is possible in even number of spatial dimensions if the background is not the Minkowski but the de Sitter spacetime and the gravity theory is massive gravity with a tuned mass in terms of the cosmological constant. Mass and the cosmological constant conspire to get rid of the anomalous dispersion and restore Huygens' principle.

gr-qc↗

arXiv2021

Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism

We study the momentum and Hamiltonian constraints of vacuum Einstein equations, within the Bowen-York formalism, for two interacting black holes in close separation, with anti-parallel spins and anti-parallel linear momenta. We give an analytical solution using perturbation theory. We also compute the location and the shape of the apparent horizon which generically depend on all the parameters, angles and the separation between the black holes. Our solution only works for distances far away from the black holes. To gain more insight close to the black holes, one has to go to the higher orders in perturbation theory, which is a rather cumbersome process. But the solution presented here can be of some use for numerical computations as the latter should match our result for the described problem.

gr-qc↗

arXiv2021

Basics of Apparent Horizons in Black Hole Physics

Event Horizon, a null hypersurface defining the boundary of the black hole region of a spacetime, is not particularly useful for evolving black holes since it is non-local in time. Instead, one uses the more tangible concept of Apparent Horizon for dynamical black holes out there in the sky that do all sorts of things: evolve, merge and feed on the environment. Event Horizon, being a gauge-independent, global property of the total spacetime is easy to define and locate in the stationary case; on the other hand, Apparent Horizon depends on the embedding of the surface in spacetime and hence it is somewhat tricky to define. But for numerical simulations in General Relativity, locating the Apparent Horizon helps one to excise the black hole region and the singularity to have a stable computation. Moreover, for stationary solutions the two horizons match. Here we give a detailed pedagogical exposition of the subject and work out the non-trivial case of a slowly moving and spinning black hole.

gr-qc↗

arXiv2021

Einstein-Yang-Mills Theory: Gauge Invariant Charges and Linearization Instability

We construct the gauge-invariant electric and magnetic charges in Yang-Mills theory coupled to cosmological General Relativity (or any other geometric gravity), extending the flat spacetime construction of Abbott and Deser. For non-vanishing background gauge fields, the charges receive non-trivial contribution from the gravity part. In addition, we study the constraints on the first order perturbation theory and establish the conditions for linearization instability: that is the validity of the first order perturbation theory.

hep-th↗

arXiv2020

Approximate analytical description of apparent horizons for initial data with momentum and spin

We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent horizon and show the dependence of its shape on the angle between the spin and the linear momentum. In particular a dimple, whose location depends on the mentioned angle, arises on the 2-sphere geometry of the apparent horizon. We exclusively work in the case of conformally flat initial metrics.

gr-qc↗

arXiv2020

Bowen-York Model Solution Redux

Initial value problem in General Relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between $[0, 0.592)$. This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is $59.2 \%$ of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.

gr-qc↗

arXiv2020

Energy and Angular Momentum in D dimensional Kerr-AdS black holes-new formulation

Recently it was shown that the conserved charges of asymptotically anti de Sitter spacetimes can be written in an explicitly gauge-invariant way in terms of the linearized Riemann tensor and the Killing vectors. Here we employ this construction to compute the mass and angular momenta of the D dimensional Kerr-AdS black holes, which is one of the most remarkable Einstein metrics generalizing the four dimensional rotating black hole.

hep-th↗

arXiv2019

Non-stationary Energy in General Relativity

Using the time evolution equations of (cosmological) General Relativity in the first order Fischer-Marsden form, we construct an integral that measures the amount of non-stationary energy on a given spacelike hypersurface in $D$ dimensions. The integral vanishes for stationary spacetimes; and with a further assumption, reduces to Dain's invariant on the boundary of the hypersurface which is defined with the Einstein constraints and a fourth order equation defining approximate Killing symmetries.

gr-qc↗

arXiv2019

Second Order Gauge Invariant Perturbation Theory and Conserved Charges in Cosmological Einstein's Gravity

Recently a new approach in constructing the conserved charges in cosmological Einstein's gravity was given. In this new formulation, instead of using the explicit form of the field equations a covariantly conserved rank four tensor was used. In the resulting charge expression, instead of the first derivative of the metric perturbation, the linearized Riemann tensor appears along with the derivative of the background Killing vector fields. Here we give a detailed analysis of the first order and the second order perturbation theory in a gauge-invariant form in cosmological Einstein's gravity. The linearized Einstein tensor is gauge-invariant at the first order but it is not so at the second order, which complicates the discussion. This method depends on the assumption that the first order metric perturbation can be decomposed into gauge-variant and gauge-invariant parts and the gauge-variant parts do not contribute to physical quantities.

hep-th↗

arXiv2019

Second Order Perturbation Theory in General Relativity: Taub Charges as Integral Constraints

In a nonlinear theory, such as General Relativity, linearized field equations around an exact solution are necessary but not sufficient conditions for linearized solutions. Therefore, the linearized field equations can have some solutions which do not come from the linearization of possible exact solutions. This fact can make the perturbation theory ill-defined, which would be a problem both at the classical and semiclassical quantization level. Here we study the first and second order perturbation theory in cosmological Einstein gravity and give the explicit form of the integral constraint, which is called the Taub charge, on the first order solutions for spacetimes with a Killing symmetry and a compact hypersurface without a boundary.

hep-th↗