arXiv subjects

Hari Kunduri

Publications and source records attributed to Hari Kunduri.

14 recordsLinked to original sources

arXiv2026

A Comparison Theorem For the Mass of ALE and ALF Toric 4-Manifolds

We establish sharp lower bounds for the mass of asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) toric 4-manifolds, in terms of equilibrium geometries consisting of gravitational instantons. More precisely, the mass of a complete ALE or ALF toric 4-manifold with nonnegative scalar curvature is bounded below by a sum comprised of the following quantities: the mass of the corresponding toric gravitational instanton having the same orbit space (rod) structure as the original ALE/ALF manifold, and an expression determined by the conical angle defects of totally geodesic 2-spheres within the instanton that serve as generators for its second homology. The inequality may be generalized to the situation in which the ALE/ALF manifold also possesses conical singularities as well as orbifold singularities, and it suggests a refined notion of `total mass' in which the result simply states that the total mass of the ALE/ALF manifold is not less than that of the corresponding gravitational instanton. Furthermore, we prove rigidity for these statements, namely the inequality is saturated only when the ALE/ALF manifold is Ricci flat and in fact agrees with the corresponding instanton. These results may be viewed in the context of positive mass theorems, providing an explanation of how positivity can fail in the ALE/ALF setting. Moreover, the main theorem may be interpreted as yielding a variational characterization of the relevant toric gravitational instantons.

math.DG↗

arXiv2026

New quasi-Einstein metrics on a two-sphere

We construct all axi-symmetric non-gradient $m$-quasi-Einstein structures on a two-sphere. This includes the spatial cross-section of the extreme Kerr black hole horizon corresponding to $m=2$, as well as a family of new regular metrics with $m\neq 2$ given in terms of hypergeometric functions. We also show that in the case $m=-1$ with vanishing cosmological constant the only orientable compact solution in dimension two is the flat torus, which proves that there are no compact surfaces with a metrisable affine connection with skew Ricci tensor.

math.DG↗

arXiv2025

Distorted black ring with rotation on the two-sphere

We construct a stationary black ring spacetime with rotation only along the $S^2$ direction that is free of conical singularities. We use a solution-generating technique to add external gravitational fields and show these can be used to remove conical singularities from an asymptotically flat black ring with a rotating $S^2$.

gr-qc↗

arXiv2024

The Spacetime Penrose Inequality for Cohomogeneity One Initial Data

We prove the spacetime Penrose inequality for asymptotically flat $2(n+1)$-dimensional initial data sets for the Einstein equations, which are invariant under a cohomogeneity one action of $\mathrm{SU}(n+1)$. Analogous results are obtained for asymptotically hyperbolic initial data that arise as spatial hypersurfaces in asymptotically Anti de-Sitter spacetimes. More precisely, it is shown that with the dominant energy condition, the total mass is bounded below by an explicit function of the outermost apparent horizon area. Furthermore, the inequality is saturated if and only if the initial data isometrically embed into a Schwarzschild(-AdS) spacetime. This generalizes the only previously known case of the conjectured spacetime Penrose inequality, established under the assumption of spherical symmetry. Additionally, in the time symmetric case, we observe that the inequality holds for $4(n+1)$-dimensional and 16-dimensional initial data invariant under cohomogeneity one actions of $\mathrm{Sp}(n+1)$ and $\mathrm{Spin}(9)$, respectively, thus treating the inequality for all cohomogeneity one actions in this regime.

math.DG↗

arXiv2024

Distorted static black holes with a bubble

We construct a family of local static, vacuum five-dimensional solutions with two commuting spatial isometries describing a black hole with a $S^3$ horizon and a 2-cycle `bubble' in the domain of outer communications. The solutions are obtained by adding distortions to an asymptotically flat seed solution. We show that the conical singularities in the undistorted geometry can be removed by an appropriate choice of the distortion.

gr-qc↗

arXiv2023

Existence and Uniqueness of Stationary Solutions in 5-Dimensional Minimal Supergravity

We study the problem of stationary bi-axially symmetric solutions of the $5$-dimensional minimal supergravity equations. Essentially all possible solutions with nondegenerate horizons are produced, having the allowed horizon cross-sectional topologies of the sphere $S^3$, ring $S^1\times S^2$, and lens $L(p,q)$, as well as the three different types of asymptotics. The solutions are smooth apart from possible conical singularities at the fixed point sets of the axial symmetry. This analysis also includes the solutions known as solitons in which horizons are not present but are rather replaced by nontrivial topology called bubbles which are sustained by dipole fluxes. Uniqueness results are also presented which show that the solutions are completely determined by their angular momenta, electric and dipole charges, and rod structure which fixes the topology. Consequently we are able to identify the finite number of parameters that govern a solution. In addition, a generalization of these results is given where the spacetime is allowed to have orbifold singularities.

gr-qc↗

arXiv2022

Exotic marginally outer trapped surfaces in rotating spacetimes of any dimension

The recently developed MOTSodesic method for locating marginally outer trapped surfaces was effectively restricted to non-rotating spacetimes. In this paper we extend the method to (multi-)axisymmetric time slices of (multi-)axisymmetric spacetimes of any dimension. We then apply this method to study marginally outer trapped surfaces (MOTSs) in the BTZ, Kerr and Myers-Perry black holes. While there are many similarities between the MOTSs observed in these spacetimes and those seen in Schwarzschild and Reissner-Nordström, details of the more complicated geometries also introduce some new, previously unseen, behaviours.

gr-qc↗

arXiv2021

Cosmic Cloaking of Rich Extra Dimensions

We present arguments that show why it is difficult to see \emph{rich} extra dimensions in the Universe. More precisely, we study the conditions under which significant size and variation of the extra dimensions in a Kaluza-Klein compactification lead to a black hole in the lower dimensional theory. The idea is based on the hoop (or trapped surface) conjecture concerning black hole existence, as well as on the observation that dimensional reduction on macroscopically large, twisted, or highly dynamical extra dimensions contributes positively to the energy density in the lower dimensional theory and can induce gravitational collapse. We analyze these conditions and find that in an idealized scenario a threshold for the size exists, on the order of $10^{-19}m$, such that extra dimensions of length above this level must lie inside black holes, thus shielding them from the view of outside observers. The threshold is highly dependent on the size of the Universe, leading to the speculation that in the early stages of evolution truly macroscopic and large extra dimensions would have been visible.

hep-th↗

arXiv2021

Existence and Uniqueness of Near-Horizon Geometries for 5-Dimensional Black Holes

We prove existence of all possible bi-axisymmetric near-horizon geometries of 5-dimensional minimal supergravity. These solutions possess the cross-sectional horizon topology $S^3$, $S^1\times S^2$, or $L(p,q)$ and come with prescribed electric charge, two angular momenta, and a dipole charge (in the ring case). Moreover, we establish uniqueness of these solutions up to an isometry of the symmetric space $G_{2(2)}/SO(4)$.

hep-th↗

arXiv2021

Bounding Horizon Area by Angular Momentum, Charge, and Cosmological Constant in 5-Dimensional Minimal Supergravity

We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces can have the nontrivial topologies $S^1 \times S^2$ and $L(p,q)$. In addition to two angular momenta, they may be characterized by `dipole charge' as well as electric charge. We show that the unique geometries which saturate the inequalities are the horizon geometries corresponding to extreme black hole solutions. Analogous inequalities which also include contributions from a positive cosmological constant are also presented.

hep-th↗

arXiv2021

Eigenvalues of the MOTS stability operator for slowly rotating Kerr black holes

We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass $|a| \ll M$. We prove that each eigenvalue depends analytically on $a$ (in a neighbourhood of $a=0$), and compute its first nonvanishing derivative. Recalling that $a=0$ corresponds to the Schwarzschild solution, where each eigenvalue has multiplicity $2\ell+1$, we find that this degeneracy is completely broken for nonzero $a$. In particular, for $0 < |a| \ll M$ we obtain a cluster consisting of $\ell$ distinct complex conjugate pairs and one real eigenvalue. As a special case of our results, we get a simple formula for the variation of the principal eigenvalue. For perturbations that preserve the total area or mass of the black hole, we find that the principal eigenvalue has a local maximum at $a=0$. However, there are other perturbations for which the principal eigenvalue has a local minimum at $a=0$.

gr-qc↗

arXiv2017

Mass-Angular Momentum Inequality For Black Ring Spacetimes

The inequality $m^3\geq \frac{27π}{4} |\mathcal{J}_{2}||\mathcal{J}_{1}-\mathcal{J}_{2}|$ relating total mass and angular momenta, is established for (possibly dynamical) spacetimes admitting black holes of ring ($S^1\times S^2$) topology. This inequality is shown to be sharp in the sense that it is saturated precisely for the extreme Pomeransky-Sen'kov black ring solutions. The physical significance of this inequality and its relation to new evidence of black ring instability, as well as the standard picture of gravitational collapse, are discussed.

hep-th↗

arXiv2017

Relating Mass to Angular Momentum and Charge in 5-Dimensional Minimal Supergravity

We prove a mass-angular momentum-charge inequality for a broad class of maximal, asymptotically flat, bi-axisymmetric initial data within the context of five-dimensional minimal supergravity. We further show that the charged Myers-Perry black hole initial data are the unique minimizers. In addition, we establish a rigidity statement for the relevant BPS bound, and give a variational characterization of BMPV black holes.

hep-th↗

arXiv2017

Proof of the Mass-Angular Momentum Inequality for Bi-Axisymmetric Black Holes With Spherical Topology

We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum inequality in this setting for 5-dimensional spacetimes. That is, all data in this class satisfy the inequality $m^3\geq \frac{27π}{32}\left(|\mathcal{J}_1|+|\mathcal{J}_2|\right)^2$, where $m$ and $\mathcal{J}_i$, $i=1,2$ are the total mass and angular momenta of the spacetime. Moreover, equality holds if and only if the initial data set is isometric to the canonical slice of an extreme Myers-Perry black hole.

gr-qc↗