#### Alladi Ramakrishnan Hall

#### Spherically symmetric vacuum spacetimes in first order gravity: Fate of curvature singularities

#### Sandipan Sengupta

##### IIT Kharagpur

*A class of spherically symmetric vacuum solutions in first order gravity theory is presented for which the metric exhibits two phases in two different regions. While it is invertible (i.e., determinant is non-zero) and is equivalent to the Schwarzschild exterior geometry in one region, it is noninvertible in the other whose geometry is different from the interior Schwarzschild spacetime. For these vacuum geometries, all the curvature tensor components remain finite everywhere. Such a scenario is untenable in Einsteinian gravity which corresponds to the phase based on invertible metrics only. For these configurations, it is possible to identify a parameter analogous to the `Schwarzschild mass' whose origin is purely geometric or torsional.*

Done