arXiv subjects

Vardarajan Suneeta

Publications and source records attributed to Vardarajan Suneeta.

15 recordsLinked to original sources

arXiv2026

Computing nonlinearity ratios using second order black hole perturbation theory

We revisit an analytical approximation scheme for computing nonlinearity ratios involving quadratic quasinormal modes (QQNMs). We compute these ratios for the general case when the QQNM is not one of the linear QNMs, for the $(l,m)$ channel $(2,2) \times (2,2) \to (4,4)$. We find an excellent match with numerical simulations. We also discuss where and why the method can fail, for example, for the channel $(2,0) \times (2,0) \to (2,0)$ where we can only get crude estimates for the nonlinearity ratio. Motivated by recent studies on nonlinear ringdown at the horizon, we also compute the nonlinearity ratios at the horizon. We find that the ratio both at the horizon and infinity is insensitive to different choices of regularization of the source term in the second order perturbations. We also discuss amplitudes of QQNMs sourced by linear overtones. Finally, we discuss the issues that must be resolved within this method to do precision analysis of nonlinear ringdown.

gr-qc↗

arXiv2025

Causal Structure of Higher Curvature Gravity

In this paper, we analyze the causal structure of Generalized Quadratic Gravity (GQG) and Einsteinian Cubic Gravity (ECG). It is well known that gravitons in higher-curvature theories can exhibit superluminal propagation, rendering the conventional definition of causal structures based on null curves inadequate. Instead, the causal structure must be defined using the fastest propagating modes, which travel along characteristic surfaces. The superluminal propagation in higher-curvature theories has significant implications for black holes. Specifically, if the Killing horizon of a black hole is not a characteristic surface corresponding to the fastest propagating mode, the horizon can no longer function as a causal barrier. Our analysis demonstrates that GQG with a genuine fourth-order equation of motion possesses only null characteristics, implying that the horizon is a characteristic surface. Furthermore, we perform a detailed characteristic analysis of ECG. We show that while all null surfaces are characteristic surfaces in ECG, the converse is not true - there exist non-null characteristic surfaces. In particular, we identify a non-null characteristic surface in a Type N spacetime in the algebraic classification of spacetimes. Despite the existence of multiple characteristic surfaces in ECG, we establish that the black hole horizon remains a characteristic surface.

hep-th↗

arXiv2024

A local Generalized second law in crossed product constructions

In this paper, we show a local generalized second law (the generalized entropy is nondecreasing) in crossed product constructions for maximally extended static and Kerr black holes using modular theory. The new ingredient is the use of results from a recent paper discussing the entropy of the algebra of operators in subregions of arbitrary spacetimes. These results rely on an assumption which we show is true in our setting. However, we do assume as in that paper, that the gravitational constraints are implemented on each partial Cauchy slice. We employ a slight generalization of the construction, by including an observer degree of freedom even for wedge shaped regions with an asymptotic boundary. In the last part of the paper, we look at modular Hamiltonians of deformed half-spaces in a class of static spacetimes, including the Schwarzschild spacetime. These are computed using path integrals, and we primarily compute them to investigate whether these non-local modular Hamiltonians can be made local by subtracting off pieces from the algebra and its commutant, as has been surmised in the literature. Along the way, the averaged null energy condition (ANEC) also follows in this class of spacetimes.

hep-th↗

arXiv2023

Generalized Entropy in Higher Curvature Gravity And Entropy of Algebra of Observables

Recently, Chandrasekaran, Penington and Witten (CPW) have shown that the generalized entropy of the Schwarzschild black hole at the bifurcation surface equals the entropy of an extended von Neumann algebra of quantum observables in the black hole exterior, in semiclassical Einstein gravity. They also derive a version of the Generalized Second law. We generalize these results to a static black hole in an arbitrary diffeomorphism invariant theory of gravity. Thus, a version of the Generalized second law for an arbitrary diffeomorphism invariant theory of gravity follows.

hep-th↗

arXiv2022

A note on the action with the Schwarzian at the stretched horizon

In this paper, we discuss the quantization of an interesting model of Carlip which appeared recently. It shows a way to associate boundary degrees of freedom to the stretched horizon of a stationary non-extremal black hole, as has been done in JT gravity for near-extremal black holes. The path integral now contains an integral over the boundary degrees of freedom, which are time reparametrizations of the stretched horizon keeping its length fixed. These boundary degrees of freedom can be viewed as elements of $Diff(S^1)/S^1$, which is the coadjoint orbit of an ordinary coadjoint vector under the action of the Virasoro group. From the symplectic form on this manifold, we obtain the measure in the boundary path integral. Doing a one-loop computation about the classical solution, we find that the one-loop answer is not finite, signalling that either the classical solution is unstable or there is an indefiniteness problem with this action, similar to the conformal mode problem in quantum gravity. Upon analytically continuing the field, the boundary partition function we get is independent of the inverse temperature and does not contribute to the thermodynamics at least at one-loop. This is in contrast to the study of near-extremal black holes in JT gravity, where the entire contribution to thermodynamics is from boundary degrees of freedom.

hep-th↗

arXiv2022

Study of Semiclassical Instability of the Schwarzschild AdS Black Hole in the Large $D$ Limit

We analyze the semiclassical stability of the Schwarzschild AdS black hole in the Euclidean partition function approach. We perform this computation in the large $D$ limit and focus on scalar perturbations. We obtain the equations for non-spherically symmetric scalar perturbations in a simple form. For a class of perturbations stability is demonstrated by the S-deformation method. For some other classes we rule out unstable modes of $\mathcal{O}(D^2)$. We also analyze the spherically symmetric perturbations and demonstrate the appearance of an unstable mode for small black holes in the large $D$ limit. We obtain an expression for the eigenvalue corresponding to the unstable mode to next to leading order in a $1/D$ expansion. This result agrees with a previously obtained numerical bound on this eigenvalue. For cosmological constant zero, our answer matches a previous result obtained for the corresponding eigenvalue for the $D$ dimensional Schwarzschild-Tangherlini black hole to next to leading order in a $1/D$ expansion.

gr-qc↗

arXiv2021

Some results in AdS/BCFT

In this paper, we study the $AdS/BCFT$ construction in $AdS_3$ and the BTZ black hole spacetime. We find a new solution to the equation for the End of the World (EoW) brane. The induced metric on this solution is that of $dS_2$ with an isometry group identical to that of $AdS_2$ and the symmetry group of the corresponding BCFT. It also leads to a corresponding EoW brane in the non-rotating BTZ background which is consistent with the periodic identifications of the non-rotating BTZ black hole. The new solution generalizes easily to higher dimensions.

hep-th↗

arXiv2021

The Black hole Black string phase transition in Einstein-Gauss-Bonnet gravity

We investigate the presence of a black hole black string phase transition in Einstein Gauss Bonnet (EGB) gravity in the large dimension limit. The merger point is the static spacetime connecting the black string phase with the black hole phase. We consider several ranges of the Gauss-Bonnet parameter. We find that there is a range when the Gauss-Bonnet corrections are subordinate to the Einstein gravity terms in the large dimension limit, and yet the merger point geometry does not approach a black hole away from the neck. We cannot rule out a topology changing phase transition as argued by Kol. However as the merger point geometry does not approach the black hole geometry asymptotically it is not obvious that the transition is directly to a black hole phase. We also demonstrate that for another range of the Gauss-Bonnet parameter, the merger point geometry approaches the black hole geometry asymptotically when a certain parameter depending on the Gauss-Bonnet parameter $α$ and on the parameters in the Einstein-Gauss-Bonnet black hole metric is small enough.

gr-qc↗

arXiv2020

Nonlinear perturbations of higher dimensional anti-de Sitter spacetime

We study nonlinear gravitational perturbations of vacuum Einstein equations, with $Λ<0$ in $(n+2)$ dimensions, with $n>2$, generalizing previous studies for $n=2$. We follow the formalism by Ishibashi, Kodama and Seto to decompose the metric perturbations into tensor, vector and scalar sectors, and simplify the Einstein equations. The tensor perturbations are the new feature of higher dimensions. We render the metric perturbations asymptotically anti-de Sitter by employing a suitable gauge choice for each of the sectors. Finally, we analyze the resonant structure of the perturbed equations at second order for the five dimensional case, by a partial study of single mode tensor-type perturbations at the linear level. For the cases we studied, resonant terms vanish at second order.

gr-qc↗

arXiv2019

Gravitational Perturbations in a cavity: Nonlinearities

Motivated by recent studies of nonlinear perturbations of asymptotically anti-de Sitter spacetimes, we study gravitational perturbations of $(n+2)$ dimensional Minkowski spacetime with a spherical Dirichlet wall. By considering the tensor, vector and scalar perturbations on the $n$ sphere, we present simplified nonhomogeneous equations at arbitrary order in weakly nonlinear perturbation theory for each sector. A suitable choice of perturbative variables is required at higher orders to simplify the expression for the boundary conditions and to expand the variables in terms of linear order eigenfunctions. Finally we comment on the nonlinear stability of the system. Some of the tools used can easily be generalized to study nonlinear perturbations of anti-de Sitter spacetime.

gr-qc↗

arXiv2018

Schwarzschild-Tangherlini quasinormal modes at large $D$ revisited

The large dimension ($D$) limit of general relativity has been used in problems involving black holes as an analytical approximation tool. Further it has been proposed that both linear and nonlinear problems involving black holes can be systematically studied in a $1/D$ expansion. Certain quasinormal modes of higher-dimensional Schwarzschild black holes with $ω\sim \mathcal{O}(1)$ were studied in the large $D$ limit using a $1/D$ expansion for the mode function. In this paper, we revisit this linear perturbation problem and obtain an analytical equation for the vector quasinormal modes $ω\sim \mathcal{O}(1)$ in the large $D$ limit, without using a $1/D$ expansion for the mode function. This can be used to compute quasinormal modes to next to leading order in $1/D$. We also compute vector and scalar quasinormal modes with $ω\sim \mathcal{O}(D)$ in the Laplace transform approach in the large $D$ limit. We discuss the useful features of this approach specifically in the large $D$ limit.

hep-th↗

arXiv2016

Non-spherically symmetric black string perturbations in the large D limit

We consider non-spherically symmetric perturbations of the uncharged black string/flat black brane in the large dimension (D) limit of general relativity. We express the perturbations in a simplified form using variables introduced by Ishibashi and Kodama. We apply the large D limit to the equations, and show that this leads to decoupling of the equations in the near-horizon and asymptotic regions. It also enables use of matched asymptotic expansions to obtain approximate analytical solutions and to analyze stability of the black string/brane. For a large class of non-spherically symmetric perturbations, we prove that there are no instabilities in the large D limit. For the rest, we provide additional matching arguments that indicate that the black string/brane is stable. In the \emph{static} limit, we show that for \emph{all} non-spherically symmetric perturbations, there is no instability. This is proof that the Gross-Perry-Yaffe mode for semiclassical black hole perturbations is the unique unstable mode even in the large D limit. This work is also a direct analytical indication that the only instability of the black string is the Gregory-Laflamme instability.

hep-th↗

arXiv2015

Necessary conditions for an AdS-type instability

In this work, we analyze the necessary conditions for a nonlinear AdS-type instability in the gravity-scalar field system. In particular, we discuss the necessary conditions for a cascade of energy to higher modes by applying results in KAM theory. Our analytical framework explains numerical observations of instability of spacetimes even when the spectrum is only asymptotically resonant, and the fact that a minimum field amplitude is needed to trigger it. Our framework can be applied for similar stability analyses of fields in (locally) asymptotically AdS spacetimes. We illustrate this with the example of the AdS soliton. Further, we conjecture on the possible reasons for quasi-periodic behaviour observed in perturbations of AdS spacetime. Certain properties of the eigenfunctions of the linear system dictate whether there will be localization in space leading to black hole formation. These properties are examined using the asymptotics of Jacobi polynomials. Finally we discuss recent results on the AdS instability in Einstein-Gauss-Bonnet gravity in light of our work.

gr-qc↗

arXiv2015

The sausage sigma model revisited

Fateev's sausage sigma models in two and three dimensions are known to be integrable. We study their stability under RG flow in the target space by using results from the mathematics of Ricci flow. We show that the three dimensional sausage is unstable, whereas the two dimensional sausage appears to be stable at least at leading order as it approaches the sphere. We speculate that the stability results obtained are linked to the classification of ancient solutions to Ricci flow (i.e., sigma models which are nonperturbative in the IR) in two and three dimensions. We also describe a class of perturbations of the three dimensional sausage (with the same continuous symmetries) which remarkably decouple. This indicates that there could be a new solution to RG flow which is described at least perturbatively as a deformation of the sausage.

hep-th↗

arXiv2012

Stability analysis of the Witten black hole (cigar soliton) under world-sheet RG flow

We analyze the stability of the Euclidean Witten black hole (the cigar soliton in mathematics literature) under first-order RG (Ricci) flow of the world-sheet sigma model. This analysis is from the target space point of view. We find that the Witten black hole has no unstable normalizable perturbative modes in a linearized mode analysis in which we consider circularly symmetric perturbations. Finally, we discuss a result from mathematics that implies the existence of a non-normalizable mode of the Witten black hole under which the geometry flows to the sausage solution studied by Fateev, Onofri and Zamolodchikov.

hep-th↗