# A General Relativistic Approach to Small-Scale Structure Formation

## TL;DR

This paper introduces a general relativistic toy model for galaxy formation, demonstrating the feasibility of equilibrium configurations through explicit spacetime matching, offering a new perspective beyond traditional Newtonian models.

## Contribution

It presents the first explicit general relativistic model of galaxy formation with non-singular initial conditions and equilibrium states, expanding the theoretical framework beyond Newtonian approaches.

## Key findings

- Equilibrium configurations can be formed via relativistic gravitational collapse.
- Matching different spacetime regions is feasible within the model.
- The model provides a foundation for more realistic relativistic galaxy formation scenarios.

## Abstract

We treat here general relativistically the issue of galaxy formation, which is a major problem in cosmology. While the current models use a top-hat collapse model, coupled with Newtonian virialization technique to balance the gravitationally collapsing matter cloud into a galaxy, we present here a general relativistic toy model to achieve such a purpose. We consider a relativistic gravitational collapse that begins from physically reasonable and non-singular initial conditions and that tends to an equilibrium configuration in asymptotic time. The matching of different spacetime regions is explicitly demonstrated to establish the feasibility of the model. This helps us understand better how the formation of galaxy-like objects and dark matter halos are likely to develop as the universe evolves, using a general relativistic technique. While the toy model we present here uses a somewhat simplistic collapse framework, this, however, has the potential to develop into a more realistic scenario, as we have noted. As we point out, the attractive feature here is, we have explicitly demonstrated that equilibrium configurations can be formed, with suitable matchings made, which go some way to treat the problem of galaxy formation within a full general relativity framework.