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Hari K. Kunduri

Publications and source records attributed to Hari K. Kunduri.

At least 19 recordsLinked to original sources
arXiv2026

Ovcharenko-Podolsky Einstein-Maxwell gravitational instantons

We present an explicit three-parameter family of toric Einstein-Maxwell gravitational instantons. These are complete Riemannian manifolds with vanishing scalar curvature which satisfy the Riemannian Einstein-Maxwell equations. We argue that the metric can be extended to a space with two asymptotic ends diffeomorphic to $\mathbb{H}^2 \times S^2$ with a non-collapsing two-cycle (bolt) in the bulk. The global metric is produced by suitably extending an analytic continuation of a local family of Lorentzian black hole geometries constructed by Ovcharenko-Podolsky.

gr-qc↗
arXiv2026

On the existence of toric ALE and ALF gravitational instantons

We establish existence and uniqueness results for asymptotically locally Euclidean (ALE) and asymptotically locally flat (ALF) gravitational instantons. In particular, we prove the existence of a unique, Ricci-flat, toric ALE and ALF gravitational instanton, for every admissible rod structure, that is smooth up to possible conical singularites. We also give an elementary proof that any toric ALE or ALF self-dual instanton is a multi-Eguchi-Hanson or multi-Taub-NUT solution.

math.DG↗
arXiv2025

Stability of Homogeneous minimal hypersurfaces in the Page space and $Y^{p,q}$ Sasaki-Einstein manifolds

We investigate the stability of homogeneous minimal submanifolds in two families of closed Einstein manifolds, the Page space $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$ and the Sasaki-Einstein spaces $Y^{p,q}$, which are equipped with cohomogeneity-one Einstein metrics admitting the isometric action of $SU(2) \times U(1)$ and $U(1) \times U(1) \times SU(2)$ respectively. We determine all the homogeneous, minimal hypersurfaces and explicitly compute the spectrum of their associated stability operators and determine their index.

math.DG↗
arXiv2025

On the Chen-Teo family of stationary asymptotically locally Minkowskian black holes

Chen and Teo have constructed a two-parameter family of five dimensional, stationary vacuum black hole solutions whose spatial hypersurfaces are asymptotically locally Euclidean with boundary at infinity is $L(2,1)$. Spatial cross sections of the event horizon have topology $S^3$ equipped with inhomogeneous metrics. When the mass is zero, the solution reduces to the trivial product of time with the Eguchi-Hanson gravitational instanton. We show that the spacetime metric can be smoothly extended through an event horizon and that the exterior region is stably causal. We also investigate their geometric and physical properties. In particular, we show that the Smarr relation and first law of black hole mechanics hold and compute the renormalized gravitational action.

gr-qc↗
arXiv2024

Spectrum of the Laplacian on the Page metric

We numerically construct the spectrum of the Laplacian on Page's inhomogeneous Einstein metric on $\mathbb{CP}^2 \# \overline{\mathbb{CP}}^2$ by reducing the problem to a (singular) Sturm-Liouville problem in one dimension. We perform a perturbative analysis based upon a closely related, exactly solvable problem that strongly supports our results. We also study the spectrum of the Lichnerowicz Laplacian on symmetric traceless transverse two-tensors. The method relies on both the isometries of the Page metric and pseudospectral methods to numerically solve the resulting ODEs.

math.SP↗
arXiv2023

Marginally Outer Trapped Tori in Black Hole Spacetimes

During a binary black hole merger, multiple intermediary marginally outer trapped tubes connect the initial pair of apparent horizons with the final (single) apparent horizon. The marginally outer trapped surfaces (MOTSs) that foliate these tubes can have complicated geometries as well as non-spherical topologies. In particular, toroidal MOTSs form inside both of the original black holes during the early stages of a head-on merger that starts from time-symmetric initial data [1]. We show that toroidal MOTSs also form in the maximal analytic extension of the Schwarzschild spacetime as Kruskal time advances from the $T=0$ moment of time symmetry. As for the merger simulations, they cross the Einstein-Rosen bridge and are tightly sandwiched between the apparent horizons in the two asymptotic regions at early times. This strongly suggests that their formation is a consequence of the initial conditions rather than merger physics. Finally, we consider MOTSs of spherical topology in the Kruskal-Szekeres slicing and study their properties. All of these are contained within the apparent horizon but some do not enclose the wormhole.

gr-qc↗
arXiv2023

A Penrose-type inequality with angular momenta for black holes with 3-sphere horizon topology

We establish a Penrose-type inequality with angular momenta for four dimensional, biaxially symmetric, maximal, asymptotically flat initial data sets $(M,g,k)$ for the Einstein equations with fixed angular momenta and horizon inner boundary associated to a 3-sphere outermost minimal surface. Moreover, equality holds if and only if the initial data set is isometric to a canonical time slice of a stationary Myers-Perry black hole.

gr-qc↗
arXiv2023

Supersymmetric asymptotically locally AdS$_5$ gravitational solitons

We construct supersymmetric gravitational soliton solutions of five-dimensional gauged supergravity coupled to arbitrarily many vector multiplets. The solutions are complete, globally stationary, $1/4$-BPS and are asymptotically locally AdS$_5$ with conformal boundary $\mathbb{R} \times L(p,1)$. The construction uses an $SU(2) \times U(1)-$invariant ansatz originally used by Gutowski and Reall to construct supersymmetric asymptotically AdS$_5$ black holes. A subset of these solutions have previously been obtained as supersymmetric limits of a class of local solutions of $U(1)^3$ gauged supergravity found by Chong-Cvetic-Lu-Pope, and by Lucietti-Ovchinnikov in their classification of $SU(2)$-invariant solutions of minimal gauged supergravity.

hep-th↗
arXiv2023

Phase Transitions and Stability of Eguchi-Hanson-AdS Solitons

The Eguchi-Hanson-AdS$_5$ family of spacetimes are a class of static, geodesically complete asymptotically locally AdS$_5$ soliton solutions of the vacuum Einstein equations with negative cosmological constant. They have negative mass and are parameterized by an integer $p\geq 3$ with a conformal boundary with spatial topology $L(p,1)$. We investigate mode solutions of the scalar wave equation on this background and show that, similar to AdS$_5$, the geometry admits a normal mode spectrum (i.e. solutions that neither grow or decay in time). In addition, we also discuss other geometric properties of these soliton spacetimes, including the behaviour of causal geodesics and their thermodynamic properties. We also point out a surprising connection with the AdS soliton.

gr-qc↗
arXiv2022

Static near horizon geometries and rigidity of quasi-Einstein manifolds

Static vacuum near horizon geometries are solutions $(M,g,X)$ of a certain quasi-Einstein equation on a closed manifold $M$, where $g$ is a Riemannian metric and $X$ is a closed 1-form. It is known that when the cosmological constant vanishes, there is rigidity: $X$ vanishes and consequently $g$ is Ricci flat. We study this form of rigidity for all signs of the cosmological constant. It has been asserted that this rigidity also holds when the cosmological constant is negative, but we exhibit a counter-example. We show that for negative cosmological constant if $X$ does not vanish identically, it must be incompressible, have constant norm, and be nontrivial in cohomology, and $(M,g)$ must have constant scalar curvature and zero Euler characteristic. If the cosmological constant is positive, $X$ must be exact (and vanishing if $\dim M=2$). Our results apply more generally to a broad class of quasi-Einstein equations on closed manifolds. We extend some known results for quasi-Einstein metrics with exact 1-form $X$ to the closed $X$ case. We consider near horizon geometries for which the vacuum condition is relaxed somewhat to allow for the presence of a limited class of matter fields. An appendix contains a generalization of a result of Lucietti on the Yamabe type of quasi-Einstein compact metrics (with arbitrary $X$).

math.DG↗
arXiv2022

Supersymmetric multi-charge solitons in AdS$_5$

We construct supersymmetric, asymptotically AdS$_5$ gravitational soliton solutions of five-dimensional gauged supergravity coupled to arbitrarily many vector multiplets. These generalize the supersymmetric solitons of $U(1)^3$ gauged supergravity previously constructed by Chong, Cvetic, Lu, and Pope. We show that the solitons contain evanescent ergosurfaces and give an argument that these solitons should be nonlinearly unstable.

hep-th↗
arXiv2022

Existence and uniqueness of asymptotically flat toric gravitational instantons

We prove uniqueness and existence theorems for four-dimensional asymptotically flat, Ricci-flat, gravitational instantons with a torus symmetry. In particular, we prove that such instantons are uniquely characterised by their rod structure, which is data that encodes the fixed point sets of the torus action. Furthermore, we establish that for every admissible rod structure there exists an instanton that is smooth up to possible conical singularities at the axes of symmetry. The proofs involve adapting the methods that are used to establish black hole uniqueness theorems, to a harmonic map formulation of Ricci-flat metrics with torus symmetry, where the target space is directly related to the metric (rather than auxiliary potentials). We also give an elementary proof of the nonexistence of asymptotically flat toric half-flat instantons. Finally, we derive a general set of identities that relate asymptotic invariants such as the mass to the rod structure.

math.DG↗
arXiv2021

Holographic complexity of rotating black holes

Within the framework of the "complexity equals action" and "complexity equals volume" conjectures, we study the properties of holographic complexity for rotating black holes. We focus on a class of odd-dimensional equal-spinning black holes for which considerable simplification occurs. We study the complexity of formation, uncovering a direct connection between complexity of formation and thermodynamic volume for large black holes. We consider also the growth-rate of complexity, finding that at late-times the rate of growth approaches a constant, but that Lloyd's bound is generically violated.

hep-th↗
arXiv2020

Abelian instantons over the Chen-Teo AF geometry

We classify finite energy harmonic 2-forms on the asymptotically flat gravitational instanton constructed by Chen and Teo. We prove that every $U(1)$-bundle admits a unique anti-self-dual Yang-Mills instanton (up to gauge equivalence) which we describe explicitly in coordinates. As an application, we compute the classical partition function for Maxwell theory with theta term.

math.DG↗
arXiv2020

Holographic Complexity and Thermodynamic Volume

We study the holographic complexity conjectures for rotating black holes, uncovering a relationship between the complexity of formation and the thermodynamic volume of the black hole. We suggest that it is the thermodynamic volume and not the entropy that controls the complexity of formation of large black holes in both the Complexity Equals Action and Complexity Equals Volume proposals in general. Our proposal reduces to known results involving the entropy in settings where the thermodynamic volume and entropy are not independent, but has broader scope. Assuming a conjectured inequality is obeyed by the thermodynamic volume, we establish that the complexity of formation is bounded from below by the entropy for large black holes.

hep-th↗
arXiv2020

Slow decay of waves in gravitational solitons

We consider a family of globally stationary (horizonless), asymptotically flat solutions of five-dimensional supergravity. We prove that massless linear scalar waves in such soliton spacetimes cannot have a uniform decay rate faster than inverse logarithmically in time. This slow decay can be attributed to the stable trapping of null geodesics. Our proof uses the construction of quasimodes which are time periodic approximate solutions to the wave equation. The proof is based on previous work to prove an analogous result in Kerr-AdS black holes \cite{holzegel:2013kna}. We remark that this slow decay is suggestive of an instability at the nonlinear level.

gr-qc↗
arXiv2019

Chemistry and Complexity for Solitons in AdS$_5$

Minimal $D=5$ supergravity admits asymptotically globally AdS$_5$ gravitational solitons (strictly stationary, geodesically complete spacetimes with positive mass). We show that, like asymptotically flat gravitational solitons, these solutions satisfy mass and mass variation formulas analogous to those satisfied by AdS black holes. A thermodynamic volume associated to the non-trivial topology of the spacetime plays an important role in this construction. We then consider these solitons within the holographic ``complexity equals action'' and ``complexity equals volume'' conjectures as simple examples of spacetimes with nontrivial rotation and topology. We find distinct behaviours for the volume and action, with the counterterm for null boundaries playing a significant role in the latter case. For large solitons we find that both proposals yield a complexity of formation proportional to a power of the thermodynamic volume, $V^{3/4}$. In fact, up to numerical prefactors, the result coincides with the analogous one for large black holes.

hep-th↗