# Reductions of Topologically Massive Gravity I: Hamiltonian Analysis of The Second Order Degenerate Lagrangians

## TL;DR

This paper analyzes the Hamiltonian formulations of certain second order degenerate Lagrangians in topologically massive gravity, employing Dirac-Bergmann and Gotay-Nester-Hinds algorithms to explore their constraints and unified formalism.

## Contribution

It provides a detailed Hamiltonian analysis of degenerate Lagrangians in topologically massive gravity using advanced constraint algorithms.

## Key findings

- Derived total Hamiltonian functions for the Lagrangians.
- Identified the constraint structures using Dirac-Bergmann algorithm.
- Explored the unified formalism via Skinner-Rusk approach.

## Abstract

We study the Hamiltonian formalisms of the second order degenerate Cl\`ement and Sar{\i}o\u{g}lu-Tekin Lagrangians. The Dirac-Bergmann constraint algorithm is employed while arriving at the total Hamiltonian functions and the Hamilton's equations on the associated momemtum phase spaces whereas the Gotay-Nester-Hinds algorithm is run while investigating the Skinner-Rusk unified formalism on the proper Whitney bundles.