TIME-SYMMETRIC INITIAL DATA SETS IN 4--D DILATON GRAVITY

TL;DR

This paper investigates time-symmetric initial data in 4D dilaton gravity, revealing effects of scalar fields on black hole properties, and constructs regular wormhole initial data with certain singularities.

Contribution

It introduces new initial data sets in dilaton gravity with multiple black holes and wormholes, highlighting scalar field effects on asymptotic properties and topology constraints.

Findings

Black hole mass and charges differ across Einstein-Rosen bridges.

Regular wormhole initial data can be constructed despite dilaton singularities.

Scalar fields impose strong topological constraints on initial data surfaces.

Abstract

I study the time--symmetric initial--data problem in theories with a massless scalar field (dilaton), free or coupled to a Maxwell field in the stringy way, finding different initial--data sets describing an arbitrary number of black holes with arbitrary masses, charges and asymptotic value of the dilaton. The presence of the scalar field gives rise to a number of interesting effects. The mass and charges of a single black hole are different in its two asymptotically flat regions across the Einstein--Rosen bridge. The same happens to the value of the dilaton at infinity. This forbids the identification of these asymptotic regions in order to build (Misner) wormholes in the most naive way. Using different techniques, I find regular initial data for stringy wormholes. The price payed is the existence singularities in the dilaton field. The presence of a single--valued scalar seems to constrain strongly the allowed topologies of the initial space--like surface. Other kinds of scalar fields (taking values on a circle or being defined up to an additive constant) are also briefly considered.