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# Atlantic GR Seminar: Jinzhao Wang (ETH Zurich) and Saikat Mondal (MUN)

## November 25, 2020 @ 1:00 pm - 2:00 pm

# Outer entropy equals Bartnik-Bray inner mass, and the gravitational ant conjecture

*Jinzhao Wang (ETH Zurich)*

Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime fill-in of a given closed, connected, spacelike, codimension-two boundary. We show that for an outer-minimizing mean-convex surface, the Bartnik-Bray inner mass matches exactly with the irreducible mass corresponding to the outer entropy. The equivalence implies that the area laws derived from the outer entropy are mathematically equivalent as the monotonicity property of the quasilocal mass. It also gives rise to new bounds between entropy and the gravitational energy, which naturally gives the gravitational counterpart to Wall’s ant conjecture. We also observe that the equality can be achieved in a conformal flow of metrics, which is structurally similar to the Ceyhan-Faulkner proof of the ant conjecture. We compute the small sphere limit of the outer entropy and it is proportional to the bulk stress tensor as one would expect for a quasilocal mass.

# Marginally outer trapped (open) surfaces in Schwarzschild geometry and extreme mass ratio merger

* Saikat Mondal (MUN)*

Black holes are one of the common objects in astrophysics. Some are formed from a dying star, called a stellar black hole. There are also supermassive black holes consisting of mass millions or even billions times that of the sun. Such black holes are thought to lie at the center of almost every galaxy. In this talk we will explore the evolution of horizons of black hole mergers in a special limit called the ” extreme mass ratio” limit. For example, a supermassive black hole merges with a stellar black hole to become a single black hole. In this limit, the merging horizons can be studied with the help of simple numerics. We will discuss mainly about marginally outer trapped surfaces (MOTS). Interestingly, the MOTSs we find in our numerical analysis have an arbitrary number of self-intersections.

*The Atlantic General Relativity 2020 online postdoc/student seminar series is in the tradition of the annual AGR meetings, providing a forum not only for students and postdocs to present their research and make professional contacts but also to facilitate connections and collaborations between all Atlantic Canadian relativists. The series is student-organized and includes all areas of classical and quantum gravity. Talks will occur on the last Wednesday of every month, with each session consisting of two 30 minute talks. If you would like to attend, please email the organizers for connection details. *