Download the Linux package version of the RPCS3 Emulator and install the official PlayStation 3 system firmware downloaded directly from the PlayStation website.
For non-jailbroken users, the only legitimate ways to play PS3 titles on PS4 are:
Tools like allow you to take a standard PS2 ISO file and package it into a PS4 fPKG. The PS4's internal emulator handles the game playback. PS1/PSP to PS4 Converting
The primary obstacle is a fundamental difference in system architecture: PS3 (Cell Architecture): Uses a complex, proprietary Cell Broadband Engine. PS4 (x86 Architecture): Uses an AMD x86-64 processor, similar to modern PCs.
The scene is dynamic, and future developments like the upcoming promise to make installations even more convenient. While the path is technical, the reward is the ability to enjoy a vast library of classic titles on modern hardware. For users willing to invest the time to learn the methods and navigate the tools, the ultimate goal of PS3-to-PS4 conversion is within reach.