The fake Emerald is an object that appears in Sonic Adventure 2. It is an Emerald meant to bear similarity to a real Chaos Emerald, but it does not possess the same amount of power, and was designed to sabotage machinery.
The fake Emerald is an exact replica of the yellow Chaos Emerald. Because of this, it is a large, diamond-cut Emerald with a yellow hue, being of the same size and structure that a Chaos Emerald has. Its wavelength and properties are also identical to that of a real Chaos Emerald, enough that not even machines could tell the difference, meaning that the only way to tell the difference between the two is prior knowledge of which one is real and which is not. Also, one of the major differences between the real Chaos Emeralds is that it is designed to first reverse the energy field inside the real Chaos Emeralds and then explode (In the Japanese version, it is designed to absorb the energy of the Chaos Emeralds and explode).
The fake Emerald is less powerful than the real Chaos Emerald, although it still has chaos energy. Sonic the Hedgehog was capable of using the Emerald to execute Chaos Control. This does not appear to be a common occurrence, however, as Shadow remarks that such a feat should be impossible.
Sonic Adventure 2
The fake Emerald was created by Tails sometime after he was awarded a Chaos Emerald by Station Square for defeating the Egg Walker. Using his research on this Emerald, he developed his own artificial Chaos Emerald, one with nearly the exact same properties, but explosive when used in machinery.
Tails eventually brought the fake Emerald onto the Space Colony ARK, developing a plan to place the Emerald into the Eclipse Cannon, destroying it and halting Dr. Eggman's plan to take over the world. Sonic the Hedgehog went off to execute this plan. Meanwhile, Eggman noticed that there was an extra Chaos Emerald signature in the vicinity, and that there must have been a fake. Sonic was about to insert the Emerald into the cannon, when Eggman called him, threatening Amy Rose at gunpoint. Sonic arrived on the scene, figuring that he could easily hand Eggman the fake Emerald, save Amy and destroy the Eclipse Cannon. However, Eggman, having already suspected that Sonic and his friends were planning to use a fake emerald to undo his plans due to detecting both energy signatures from his base earlier, called his bluff, with Tails unwittingly confirming the ruse as a result, and trapped the hedgehog in a capsule which he jettisoned into space. Before the capsule could detonate, however, Sonic used Chaos Control with the fake Emerald to teleport back to the ARK in the nick of time.
Figuring he could destroy the Eclipse Cannon by manually inserting the fake Emerald into it, Sonic headed to the weapon. On his way, Shadow the Hedgehog located him, and the two begin a fight where Sonic uses the fake Emerald to do Chaos Control. After the fight, Sonic inserted the fake Emerald into the Eclipse Cannon causing disabling explosions in parts of the cannon.
In other media
In Sonic X, the fake Emerald was created by Tails during the second season in the adaptation of Sonic Adventure 2. It essentially serves the same purpose that it had in the game.
Hundreds of these Emeralds were mass produced, with similar abilities, but lesser power than the normal Chaos Emerald. They were incredibly brittle and could easily be crushed or burn out after a single use. These Emeralds were capable of inducing Chaos Control and could also initiate a Super transformation in the form of Dark Sonic. After Dark Sonic’s usage of the fake Emeralds, they were all completely rendered useless.
When Team Dark uses their Team Blast, Chaos Inferno, there is a Chaos Emerald that is used to induce the move - even if the player has yet to collect any Emeralds. Many fans have presumed that Emerald was a fake, but canonically, it likely was the green Emerald that Team Dark obtained in the cutscene before the battle against MetalSonic.
In an unused texture found inside of the game files of Sonic Adventure 2, the Fake Emerald was depicted as a white emerald instead of a yellow one. This texture was supposed to be displayed onto Eggman's monitor that he used to find out that Sonic and his friends had infiltrated the Space Colony ARK.
↑ 1.01.1Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Dr. Eggman: This is strange... it's showing energy readings from two separate Chaos Emeralds. Did they really think they could trick me with that fake Emerald?"
↑Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Sonic: Handing over the fake Emerald, I can kill two birds with one stone."
↑ 3.03.13.2Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Tails: It looks like it doesn't it? But in fact, it's a fake one that I created after researching the real Emerald! It has the same wavelength and properties but is less powerful than the real one. It's designed to reverse the energy field inside the Chaos Emeralds and blow up! It looks so real, even a machine can't tell the difference!"
↑Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Shadow: It was a Chaos Emerald, wasn't it? But, there's no way you could have activated the Chaos Control using an Emerald that's fake."
↑Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Dr. Eggman: You thought you could trick me with that Fake Emerald, didn't you? / Tails: So... how did you know it wasn't the real one? / Sonic: Tails! / Dr. Eggman: Because you just told me, fox boy!"
↑Sonic Team (3 May 2002). Sonic Adventure 2: Battle. GameCube. Sega. "Sonic: I got it! Before the cannon fires, I'll slam dunk it in there!"